Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 10 - Section 10.5 - Conic Sections - 10.5 Exercises - Page 680: 31


$y ^2 = 4x$

Work Step by Step

If a parabola is oriented upwards, the equation of the parabola is, $(x -h)^2 = 4p(y - k)$. However, if a parabola is oriented laterally, the equation of the parabola is, $(y -h)^2 = 4p(x - k)$. In the equation, the vertex of the parabola is at $(h, k) or (k,h)$ respectively. The focus is at $(h, k + p) or (k+p,h)$, respectively. So let us plug in our given points. The parabola is laterally oriented, since the focus is to the right of the vertex. The focus is $(1,0)$ and the vertex is $(0,0)$. Thus, $h=0$ and $k=0$ and $p=1$. Thus the equation is $(y -0)^2 = 4(1)(x -0)$ or $y ^2 = 4x$.
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