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
$y^2=-12(x+1)$
Multivariable Calculus, 7th Edition
by Stewart, James
Published by
Brooks Cole
ISBN 10:
0-53849-787-4
ISBN 13:
978-0-53849-787-9
Chapter 10 - Parametric Equations and Polar Coordinates - 10.5 Exercises - Page 700: 33
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