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For the following exercises, find a new representation of the given equation after rotating through the given angle . 19. 4 x 2 − x y + 4 y 2 − 2 = 0 , θ = 45 ∘

For the following exercises, find a new representation of the given equation after rotating through the given angle . 19. 4 x 2 − x y + 4 y 2 − 2 = 0 , θ = 45 ∘

College Algebra

College Algebra

1st Edition

ISBN: 9781938168383

Author: Jay Abramson

Publisher: OpenStax

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Textbook Question

Chapter 8.4, Problem 19SE

For the following exercises, find a new representation of the given equation after rotating through the given angle.

19. 4 x 2 − x y + 4 y 2 − 2 = 0 , θ = 45 ∘

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Chapter 8.4, Problem 18SE

Chapter 8.4, Problem 20SE

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Chapter 8 Solutions

College Algebra

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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=24cos Ch. 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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