## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 4 - 4.4 - Translations of Conics - 4.4 Exercises - Page 348: 41b

#### Answer

$x^2=-16400(y-4100)$

#### Work Step by Step

We are given that the focus is below the given vertex, thus, $p$ is the negative of the distance of the satellite from the center of the Earth. So, $p=-|4000+100|=-4100$ The vertex and focus have a vertical axis. The vertex is at $(0, 4100)$ Now, we will write the equation for the parabola that has a vertical axis using the vertex and $p$. $(x-h)^2=4p(y-k)$ $\implies (x-0)^2=(4)(-4100) (y-4100)$ or, $x^2=-16400(y-4100)$

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