Answer
$$y^2=-12(x+1)$$
Work Step by Step
The equation of parabola when the distance of the point $(x,y)$ from the line $x=2$ is $|x-2|$
Thus, $|x-2|=\sqrt {(x+4)^2+y^{2}}$
Hence, $y^2=-12x-12=-12(x+1)$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 10 - Parametric Equations and Polar Coordinates - 10.5 Conic Sections - 10.5 Exercises - Page 720: 33
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