Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - 10.2 The Parabola - 10.2 Assess Your Understanding - Page 647: 34

Answer

$(x-3)^2=-8y$ Latus rectum points: $(-1,-2),(7,-2)$ See graph

Work Step by Step

We are given the parabola: Focus: $(3,-2)$ Vertex: $(3,0)$ Because the vertex and the focus have the same $x$-coordinate, the parabola is vertical. Its standard equation is: $(x-h)^2=4p(y-k)$ Use the coordinates of the vertex to determine $h,k$: $(h,k)=(3,0)$ $h=3$ $k=0$ Determine $p$ using the coordinates of the focus: $(h,k+p)=(3,-2)$ $(3,0+p)=(3,-2)$ $p=-2$ Determine the parabola's equation: $(x-3)^2=4(-2)(y-0)$ $(x-3)^2=-8y$ Determine the two points defining the latus rectum: $y=-2$ $(x-3)^2=-8(-2)$ $(x-3)^2=16$ $x-3=\pm 4$ $x-3=-4\Rightarrow x_1=-1$ $x-3=4\Rightarrow x_2=7$ $\Rightarrow (-1,-2),(7,-2)$ Plot the points and graph the parabola:
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