Explanation A hyperbola with center at ( h , k ) and foci on a line parallel to the x -axis is ( x − h ) 2 a 2 − ( y − k ) 2 b 2 = 1 . Where vertices are V ( a + h , k ) and V ′ ( − a + h , k ) , foci are F ( c + h , k ) and F ′ ( − c + h , k ) , ends of the conjugate axis are B ( h , b + k ) and B ' ( h , − b + k ) , and a 2 + b 2 = c 2 is a relation between a , b , and c . A hyperbola with center at ( h , k ) and foci on a line parallel to the y -axis is ( y − k ) 2 a 2 − ( x − h ) 2 b 2 = 1 . Where vertices are V ( h , a + k ) and V ′ ( h , − a + k ) , foci are F ( h , c + k ) and F ′ ( h , − c + k ) , ends of the conjugate axis are B ( b + h , k ) and B ' ( − b + h , k ) and a 2 + b 2 = c 2 is a relation between a , b , and c . Calculation: The given equation of a hyperbola is x 2 − y 2 + 6 x + 2 y = 8 . x 2 − y 2 + 6 x + 2 y = 8 x 2 + 6 x + 9 − y 2 + 2 y − 1 = 8 + 9 − 1 ( x + 3 ) 2 − ( y − 1 ) 2 = 16 ( x − ( − 3 ) ) 2 4 2 − ( y − 1 ) 2 4 2 = 1 On comparing ( x − ( − 3 ) ) 2 4 2 − ( y − 1 ) 2 4 2 = 1 with ( x − h ) 2 a 2 − ( y − k ) 2 b 2 = 1 , the obtained observation is that a = 4 , b = 4 , h = − 3 and k = 1

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Author: Gustafson

Publisher: CENGAGE L

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Chapter 7.3, Problem 4SC

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The hyperbola of an equation x2−y2+6x+2y=8.

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Chapter 7.3, Problem 3SC

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Ch. 7.1 - Prob. 1SC Ch. 7.1 - Prob. 2SC Ch. 7.1 - Prob. 3SC Ch. 7.1 - Prob. 4SC Ch. 7.1 - Prob. 5SC Ch. 7.1 - Prob. 6SC Ch. 7.1 - Find the vertex and yintercepts of the parabola...Ch. 7.1 - Prob. 8SC Ch. 7.1 - Prob. 9SC Ch. 7.1 - Prob. 1E

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