Explanation Given: The parabola with focus at ( 2 , 1 ) and directrix is x = − 1 . Result used: “ Equation Form for Translated Parabolas: A parabola with vertex ( h , k ) has an equation of the form: ( x − h ) 2 = 4 c ( y − k ) ( Vertical axis ) ( y − k ) 2 = 4 c ( x − h ) ( Horizontal axis ) Here, focus is the distance | c | from the vertex. For vertical axis, the co-ordinates of the vertex and focus are V ( h , k ) and F ( h , k + c ) , respectively. The equation of the directrix is y = k − c . If c > 0 , the parabola opens upwards and if c < 0 , the parabola opens downwards. For horizontal axis, the co-ordinates of the vertex and focus are V ( h , k ) and F ( h + c , k ) , respectively. The equation of the directrix is x = h − c . If c > 0 , the parabola opens right and if c < 0 , the parabola opens left.” Calculation: The focus of the parabola at ( 2 , 1 ) and directrix is x = − 1 . By the above result, the equation of the directrix is x = h − c . Compare the standard form of equation of directrix with given equation x = − 1 . h − c = − 1

A Graphical Approach to College Algebra (6th Edition)

6th Edition

ISBN: 9780321920300

Author: John Hornsby, Margaret L. Lial, Gary K. Rockswold

Publisher: PEARSON

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Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 7.1, Problem 88E

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The equation of parabola with focus at (2,1) and directrix is x=−1.

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Chapter 7.1, Problem 87E

Chapter 7.1, Problem 89E

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Chapter 7 Solutions

A Graphical Approach to College Algebra (6th Edition)

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Identify the graph,...Ch. 7 - Prob. 10T Ch. 7 - Prob. 11T Ch. 7 - Prob. 12T Ch. 7 - Prob. 13T Ch. 7 - Prob. 14T Ch. 7 - Prob. 15T Ch. 7 - Prob. 16T

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The equation of parabola with focus at ( 2 , 1 ) and directrix is x = − 1 .

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Chapter 7 Solutions