College Algebra By Openstax
College Algebra By Openstax
17th Edition
ISBN: 9781506698229
Author: Jay Abramson;arizona State University
Publisher: XANEDU PUBLISHING
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Maximization
Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.
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Chapter 8.3, Problem 12SE

For the following exercises, rewrite the given equation in standard form, and then determine the vertex (V),focus (F),and directrix (d) of the parabola.

12. y = 1 4 x 2

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Chapter 8 Solutions

College Algebra By Openstax

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Ch. 8.1 - For the special case mentioned in the previous...Ch. 8.1 - What can be said about the symmetry of the graph...Ch. 8.1 - For the following exercises, determine whether the...Ch. 8.1 - For the following exercises, determine whether the...Ch. 8.1 - For the following exercises, determine whether the...Ch. 8.1 - For the following exercises, determine whether the...Ch. 8.1 - For the following exercises, determine whether the...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - For the following exercises, write the equation of...Ch. 8.1 - ALGEBRAIC For the following exercises, find the...Ch. 8.1 - For the following exercises, find the foci for the...Ch. 8.1 - For the following exercises, find the foci for the...Ch. 8.1 - For the following exercises, find the foci for the...Ch. 8.1 - For the following exercises, find the foci for the...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, use the given...Ch. 8.1 - For the following exercises, use the given...Ch. 8.1 - For the following exercises, use the given...Ch. 8.1 - For the following exercises, graph the given...Ch. 8.1 - For the following exercises, given the graph of...Ch. 8.1 - For the following exercises, given the graph of...Ch. 8.1 - For the following exercises, given the graph of...Ch. 8.1 - For the following exercises, given the graph of...Ch. 8.1 - For the following exercises, given the graph of...Ch. 8.1 - For the following exercises, find the area of the...Ch. 8.1 - For the following exercises, find the area of the...Ch. 8.1 - For the following exercises, find the area of the...Ch. 8.1 - For the following exercises, find the area of the...Ch. 8.1 - For the following exercises, find the area of the...Ch. 8.1 - Find the equation of the ellipse that will just...Ch. 8.1 - Find the equation of the ellipse that will just...Ch. 8.1 - An arch has the shape of a semi-ellipse (the top...Ch. 8.1 - An arch has the shape of a semi-ellipse. The arch...Ch. 8.1 - A bridge is to be built in the shape of a...Ch. 8.1 - A person in a whispering gallery standing at one...Ch. 8.1 - A person is standing 8 feet from the nearest wall...Ch. 8.2 - Identify the vertices and foci of the hyperbola...Ch. 8.2 - What is the standard form equation of the...Ch. 8.2 - What is the standard form equation of the...Ch. 8.2 - Graph the hyperbola given by the equation...Ch. 8.2 - Graph the hyperbola given by the standard form of...Ch. 8.2 - A design for a cooling tower project is shown in...Ch. 8.2 - Define a hyperbola in terms of its foci.Ch. 8.2 - What can we conclude about a hyperbola if its...Ch. 8.2 - What must be true of the foci of a hyperbola?Ch. 8.2 - If the transverse axis of a hyperbola is vertical,...Ch. 8.2 - Where must the center of hyperbola be relative to...Ch. 8.2 - For the following exercises, determine whether the...Ch. 8.2 - For the following exercises, determine whether the...Ch. 8.2 - For the following exercises, determine whether the...Ch. 8.2 - For the following exercises, determine whether the...Ch. 8.2 - For the following exercises, determine whether the...Ch. 8.2 - For the followung exericses, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, write the equation...Ch. 8.2 - For the following exercises, find the equations of...Ch. 8.2 - For the following exercises, find the equations of...Ch. 8.2 - For the following exercises, find the equations of...Ch. 8.2 - For the following exercises, find the equations of...Ch. 8.2 - For the following exercises, find the equations of...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, sketch a graph of the...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercise, given information...Ch. 8.2 - For the following exercises, express the equation...Ch. 8.2 - For the following exercises, express the equation...Ch. 8.2 - For the following exercises, express the equation...Ch. 8.2 - For the following exercises, express the equation...Ch. 8.2 - For the following exercises, express the equation...Ch. 8.2 - For the following exercises, a hedge is to be...Ch. 8.2 - For the following exercises, a hedge is to be...Ch. 8.2 - For the following exercises, a hedge is to be...Ch. 8.2 - For the following exercises, a hedge is to be...Ch. 8.2 - For the following exercises, a hedge is to be...Ch. 8.2 - For the following exercises, assume an object...Ch. 8.2 - For the following exercises, assume an object...Ch. 8.2 - For the following exercises, assume an object...Ch. 8.2 - For the following exercises, assume an object...Ch. 8.2 - For the following exercises, assume an object...Ch. 8.3 - Graph y2=16x . Identify and label the focus,...Ch. 8.3 - Graph x2=8y . Identify and label the focus,...Ch. 8.3 - What is the equation for the parabola with focus...Ch. 8.3 - Graph (y+1)2=4(x8) . Identify and label the...Ch. 8.3 - Graph (x+2)2=20(y3) . Identify and label the...Ch. 8.3 - Balcony-sized solar cookers have been designed for...Ch. 8.3 - Define a parabola in terms of its focus and...Ch. 8.3 - If the equation of a parabola is written in...Ch. 8.3 - If the equation of a parabola is written in...Ch. 8.3 - What is the effect on the graph of a parabola if...Ch. 8.3 - As the graph of a parabola becomes wider, what...Ch. 8.3 - For the following exercises, determine whether the...Ch. 8.3 - For the following exercises, determine whether the...Ch. 8.3 - For the following exercises, determine whether the...Ch. 8.3 - For the following exercises, determine whether the...Ch. 8.3 - For the following exercises, determine whether the...Ch. 8.3 - For the following exercises, determine whether the...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, rewrite the given...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, graph the parabola,...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, find the equation of...Ch. 8.3 - For the following exercises, the vertex and...Ch. 8.3 - For the following exercises, the vertex and...Ch. 8.3 - For the following exercises, the vertex and...Ch. 8.3 - For the following exercises, the vertex and...Ch. 8.3 - For the following exercises, the vertex and...Ch. 8.3 - The mirror in an automobile headlight has a...Ch. 8.3 - If we want to construct the mirror from the...Ch. 8.3 - A satellite dish is shaped like a paraboloid of...Ch. 8.3 - Consider the satellite dish from the previous...Ch. 8.3 - A searchlight is shaped like a paraboloid of...Ch. 8.3 - If the searchlight from the previous exercise has...Ch. 8.3 - An arch is in the shape of a parabola. It has a...Ch. 8.3 - If the arch from the previous exercise has a span...Ch. 8.3 - An object is projected so as to follow a parabolic...Ch. 8.3 - For the object from the previous exercise, assume...Ch. 8.4 - Identify the graph of each of the following...Ch. 8.4 - Rewrite the 13x263xy+7y2=16 in the x’y’system...Ch. 8.4 - Identify the conic for each of the following...Ch. 8.4 - What effect does the xyterm have on the graph of a...Ch. 8.4 - If the equation of a conic section is written in...Ch. 8.4 - If the equation of a conic section is written in...Ch. 8.4 - Given the equation ax2+4x+3y212=0 , what can we...Ch. 8.4 - For the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 , the value...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - or the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, determine which conic...Ch. 8.4 - For the following exercises, find a new...Ch. 8.4 - For the following exercises, find a new...Ch. 8.4 - For the following exercises, find a new...Ch. 8.4 - For the following exercises, find a new...Ch. 8.4 - For the following exercises, find a new...Ch. 8.4 - For the following exercises, determine the angle ...Ch. 8.4 - For the following exercises, determine the angle ...Ch. 8.4 - For the following exercises, determine the angle ...Ch. 8.4 - For the following exercises, determine the angle ...Ch. 8.4 - For the following exercises, determine the angle ...Ch. 8.4 - For the following exercises, determine the angle ...Ch. 8.4 - For the following exercises determine the angle ...Ch. 8.4 - For the following exercises determine the angle ...Ch. 8.4 - For the following exercises, rotate through the...Ch. 8.4 - For the following exercises, rotate through the...Ch. 8.4 - For the following exercises, rotate through the...Ch. 8.4 - For the following exercises, rotate through the...Ch. 8.4 - For the following exercises, rotate through the...Ch. 8.4 - For the following exercises, rotate through the...Ch. 8.4 - For the following exercises, rotate through the...Ch. 8.4 - For the following exercises, rotate through the...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises, graph the equation...Ch. 8.4 - For the following exercises. determine the angle...Ch. 8.4 - For the following exercises, determine the angle...Ch. 8.4 - For the following exercises, determine the angle...Ch. 8.4 - For the following exercises, determine the angle...Ch. 8.4 - For the following exercises, determine the angle...Ch. 8.4 - For the following exercises, determine the angle...Ch. 8.4 - For the following exercises, determine the value...Ch. 8.4 - For the following exercises, determine the value...Ch. 8.4 - For the following exercises, determine the value...Ch. 8.4 - For the following exercises, determine the value...Ch. 8.4 - For the following exercises, determine the value...Ch. 8.5 - Identify the conic with focus at the origin, the...Ch. 8.5 - Graph r=24cosCh. 8.5 - Find the polar form of the conic given a focus at...Ch. 8.5 - Convert the conic r=21+2cos to rectangular form.Ch. 8.5 - Explain how eccentricity determines which conic...Ch. 8.5 - If a conic section is written as a polar equation,...Ch. 8.5 - If a conic section is written as a polar equation,...Ch. 8.5 - If the directrix of a conic section is...Ch. 8.5 - What do we know about the focus/foci of a conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, identity the conic...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, convert the polar...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, graph the given conic...Ch. 8.5 - For the following exercises, find the polar...Ch. 8.5 - For the following exercises, find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - For the following exercises. find the polar...Ch. 8.5 - Recall from Rotation of Axes that equations of...Ch. 8.5 - Recall from Rotation of Axes that equations of...Ch. 8.5 - Recall from Rotation of Axes that equations of...Ch. 8.5 - Recall from Rotation of Axes that equations of...Ch. 8.5 - Recall from Rotation of Axes that equations of...Ch. 8 - For the following exercises. write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, graph the ellipse,...Ch. 8 - For the following exercises, graph the ellipse,...Ch. 8 - For the following exercises, graph the ellipse,...Ch. 8 - For the following exercises, graph the ellipse,...Ch. 8 - For the following exercises, use the given...Ch. 8 - For the following exercises, use the given...Ch. 8 - For the following exercises, use the given...Ch. 8 - For the following exercises. write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises. write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, graph the hyperbola,...Ch. 8 - For the following exercises, graph the hyperbola,...Ch. 8 - For the following exercises, graph the hyperbola,...Ch. 8 - For the following exercises, graph the hyperbola,...Ch. 8 - For the following exercises, find the equation of...Ch. 8 - For the following exercises, find the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, graph the parabola....Ch. 8 - For the following exercises, graph the parabola....Ch. 8 - For the following exercises, graph the parabola....Ch. 8 - For the following exercises, graph the parabola....Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, determine which of...Ch. 8 - For the following exercises, determine which of...Ch. 8 - For the following exercises, determine which of...Ch. 8 - For the following exercises, determine the angle ...Ch. 8 - For the following exercises,determine the angle ...Ch. 8 - For the following exercises, graph the equation...Ch. 8 - For the following exercises, graph the equation...Ch. 8 - For the following exercises, graph the equation...Ch. 8 - For the following exercises, given the polar...Ch. 8 - For the following exercises, given the polar...Ch. 8 - For the following exercises, given the polar...Ch. 8 - For the following exercises, given the polar...Ch. 8 - For the following exercises, graph the conic given...Ch. 8 - For the following exercises, graph the conic given...Ch. 8 - For the following exercises, graph the conic given...Ch. 8 - For the following exercises, graph the conic given...Ch. 8 - For the following exercises, given information...Ch. 8 - For the following exercises, given information...Ch. 8 - For the following exercises, write the equation in...Ch. 8 - For the following exercises, write the equation in...Ch. 8 - For the following exercises, sketch the graph,...Ch. 8 - For the following exercises, sketch the graph....Ch. 8 - For the following exercises, sketch the graph....Ch. 8 - For the following exercises, sketch the graph,...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, graph the hyperbola,...Ch. 8 - For the following exercises, graph the hyperbola....Ch. 8 - For the following exercises, graph the hyperbola,...Ch. 8 - For the following exercises. write the equation of...Ch. 8 - For the following exercises, write the equation of...Ch. 8 - For the following exercises, graph the parabola,...Ch. 8 - For the following exercises, graph the parabola,...Ch. 8 - For the following exercises, graph the parabola,...Ch. 8 - For the following exercises, graph the parabola,...Ch. 8 - For the following exercises, determine which conic...Ch. 8 - For the following exercises, determine which conic...Ch. 8 - For the following exercises, rewrite in the x’y’...Ch. 8 - For the following exercises, rewrite in the x’y’...Ch. 8 - For the following exercises, identify the conic...Ch. 8 - For the following exercises. identify the conic...Ch. 8 - For the following exercises, graph the given conic...Ch. 8 - For the following exercises, graph the given conic...Ch. 8 - For the following exercises, graph the given conic...

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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY