Explanation Given: The given equation is, y 2 + 6 y − 4 x 2 − 24 x − 63 = 0 Approach: The general equation of hyperbola not symmetric to both axes is, A ( x − h ) 2 − B ( y − k ) 2 = C Here, C is a constant term. To find the equation for the asymptotes replace the constant term of A ( x − h ) 2 − B ( y − k ) 2 = C with 0 and solve for y . A ( x − h ) 2 − B ( y − k ) 2 = 0 Calculation: Consider the given equation. y 2 + 6 y − 4 x 2 − 24 x − 63 = 0... ( 1 ) Express the given equation into the standard form by completing the square. y 2 + 6 y − 4 x 2 − 24 x − 63 = 0 ( y 2 + 6 y ) − 4 ( x 2 + 6 x ) = 63 ( y 2 + 6 y + 3 2 ) − 4 ( x 2 + 6 x + 3 2 ) = 63 + 3 2 − 4 ( 3 2 ) ( y 2 + 6 y + 9 ) − 4 ( x 2 + 6 x + 9 ) = 63 + 9 − 36 Simplify further. ( y + 3 ) 2 − 4 ( x + 3 ) 2 = 36... ( 2 ) Compare equation ( 2 ) with A ( x − h ) 2 − B ( y − k ) 2 = C . The value of h is − 3 , k is − 3 and C is 36 . Thus, the center of the hyperbola is ( h , k ) = ( − 3 , − 3 )

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ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

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To graph:

The given equation.