Explanation Given information: The given conic is ϕ ( x , y ) = a x 2 + 2 h x y + b y 2 + 2 g x + 2 f y + c = 0 . Calculation: Consider the equation ϕ ( x , y ) = a x 2 + 2 h x y + b y 2 + 2 g x + 2 f y + c = 0 . Transform the origin to the point ( m , n ) . In order to do so, make the following substitutions for x and y . x = x + m y = y + n Therefore ϕ ( x , y ) = a ( x + m ) 2 + 2 h ( x + m ) ( y + n ) + b ( y + m ) 2 + 2 g ( x + m ) + 2 f ( y + n ) + c = 0 ϕ ( x , y ) = a ( x ) 2 + 2 h x y + b ( y ) 2 + 2 x ( a m + h n + g ) + 2 y ( h m + b n + f ) + a ( m ) 2 + 2 h m n + b ( n ) 2 + 2 g m + 2 f n + c If

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 11.3, Problem 60PS

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To show: That the center of the given conic is the intersection of the lines ∂ϕ/∂x=0 and ∂ϕ/∂y=0 .

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Chapter 11.3, Problem 59PS

Chapter 11.4, Problem 1PS

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That the center of the given conic is the intersection of the lines ∂ ϕ / ∂ x = 0 and ∂ ϕ / ∂ y = 0 .

Solution Summary: The author explains that the center of a given conic is the intersection of the lines partialvarphi /

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To show: That the center of the given conic is the intersection of the lines ∂ϕ/∂x=0 and ∂ϕ/∂y=0 .

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Chapter 11 Solutions