In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( − 2 , 0 ) ; directrix the line x = 2
In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( − 2 , 0 ) ; directrix the line x = 2
In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Focus at
; directrix the line
Expert Solution
To determine
(a & b)
The equation of the parabola described and two points that define the latus rectum for the following description.
Focus at ; directrix the line .
Answer to Problem 23AYU
, Latus rectum: and .
Explanation of Solution
Given:
Focus at ; directrix at the line .
Formula used:
Vertex
Focus
Directrix
Equation
Description
Parabola, axis of symmetry is , opens left
Calculation:
From the given data we see that the focus is at and directrix is the line . The vertex is . Both vertex and lies on the vertical line (The axis of symmetry). The distance from the vertex to the focus is .
Also, because the focus lies left of the vertex, the parabola opens left.
Therefore the equation is,
To find the points that define the latus rectum, Let in the above equation.
We get,
Hence and defines the latus rectum.
Expert Solution
To determine
c.
To graph: The parabola for the equation .
Answer to Problem 23AYU
Explanation of Solution
Given:
Focus at ; vertex at .
Calculation:
The graph of the equation of the parabola is plotted below.
Using the given information D: and we have formed the equation and plotted the graph for . The focus and the vertex lie on the horizontal line.
The equation for directrix D: is shown as dotted line. The parabola opens left. The points and define the latus rectum.
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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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