Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 4 - 4.4 - Translations of Conics - 4.4 Exercises - Page 348: 40


$(x-0)^2=-8(y-2)$ or, $x^2=-8(y-2)$

Work Step by Step

We are given that the focus is above the given diretcrix; thus, $ p$ is the negative of half of the distance between the two points. So, $p=\dfrac{-1}{2}|4-0|=-2$ Since the vertex and focus have the same x-coordinate, the parabola must have a vertical axis. Now, we will write the equation for the parabola that has a vertical axis using the vertex and $p$. $(x-h)^2=4p(y-k)$ $\implies (x-0)^2=-8(y-2)$ or, $x^2=-8(y-2)$
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