Answer
$$y = \frac{1}{8}x^2 .$$
Work Step by Step
The vertex is at $(0,0)$ and the focus is at $( 0,2)$; hence, $c=2$. The parabola is vertical and opens upward and has the equation $$y =\frac{1}{4c}x^2=\frac{1}{8}x^2 .$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 22
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