Calculus (3rd Edition)

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: 24


$$y-4=\frac{1}{24}(x-3)^2 .$$

Work Step by Step

The vertex is at $(3,4)$ and the directrix is $y=-2=-c$. The parabola is vertical and opens upwards; moreover, since $c$ is the distance between the vertex and the directrix, then $c=4+2=6$. Now, the parabola has the equation $$y-k=\frac{1}{4c}(x-h)^2\Longrightarrow y-4=\frac{1}{24}(x-3)^2 .$$
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