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: 46

Answer

Vertex: $(2,-1)$ Focus: $\left(1,-1\right)$ Directrix: $x=3$ See graph

Work Step by Step

We are given the parabola: $(y+1)^2=-4(x-2)$ The standard equation is: $(y-k)^2=4p(x-h)$ Determine $h,k,p$: $h=2$ $k=-1$ $4p=-4\Rightarrow p=-1$ Determine the vertex: $(h,k)=(2,-1)$ Determine the focus: $(h+p,k)=\left(2+(-1),-1\right)=\left(1,-1\right)$ Determine the directrix: $x=h-p$ $x=2-(-1)$ $x=3$ Determine the two points defining the latus rectum: $x=1$ $(y+1)^2=4(-1)(1-2)$ $(y+1)^2=4$ $y+1=\pm 2$ $y+1=-2\Rightarrow y_1=-3$ $y+1=2\Rightarrow y_2=1$ $\Rightarrow (1,-3),(1,1)$ Plot the points, draw the directrix, and graph the parabola:
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