Answer
$y^2=-12(x+1)$
Work Step by Step
Distance of the point $(x,y)$ from the line $x=2$ is $|x-2|$
Therefore, the equation of the parabola is
$|x-2|=\sqrt {(x+4)^2+y^{2}}$
$y^2=-12x-12$
or
$y^2=-12(x+1)$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 10 - Section 10.5 - Conic Sections - 10.5 Exercises - Page 680: 33
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