(a) Explanation Definition used: Definition 1: The equation of shifted parabola with vertex V ( h , k ) is ( x − h ) 2 = 4 p ( y − k ) . Definition 2: The equation of the parabola vertex V ( 0 , 0 ) , focus F ( 0 , p ) and directrix y = − p is x 2 = 4 p y . Calculation: Simplify the parabolic equation x 2 + 2 x − 20 y + 41 = 0 into a comparable form. x 2 + 2 x − 20 y + 41 = 0 x 2 + 2 x + 1 − 20 y + 40 = 0 ( x + 1 ) 2 = 20 ( y − 2 ) Consider the equation of parabola (b) To determine To sketch: The graph of the parabola x 2 + 2 x − 20 y + 41 = 0 .

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ISBN: 9781305761049

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage

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Chapter 11.4, Problem 20E

(a)

To determine

To find: The vertex, focus and directrix of the parabola x2+2x−20y+41=0 .

(b)

To determine

To sketch: The graph of the parabola x2+2x−20y+41=0 .

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Chapter 11.4, Problem 19E

Chapter 11.4, Problem 21E

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The vertex, focus and directrix of the parabola x 2 + 2 x − 20 y + 41 = 0 .

Solution Summary: The author explains how to simplify the parabolic equation x2+2x-20y+41=0 into a comparable form.