If the equation of a hyperbola is 9x^2 - 16y^ | vedclass

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(A) Given hyperbola $H: 9x^2 - 16y^2 + 72x - 32y - 16 = 0$.Rewrite the equation by completing the squares:$9(x^2 + 8x) - 16(y^2 + 2y) = 16$$9(x+4)^2 -

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$9x^2 - 16y^2 + 72x - 32y + 272 = 0$

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(A) Given hyperbola $H: 9x^2 - 16y^2 + 72x - 32y - 16 = 0$.Rewrite the equation by completing the squares:$9(x^2 + 8x) - 16(y^2 + 2y) = 16$$9(x+4)^2 - 144 - 16(y+1)^2 + 16 = 16$$9(x+4)^2 - 16(y+1)^2 = 144$Dividing by $144$,we get $\frac{(x+4)^2}{16} - \frac{(y+1)^2}{9} = 1$.The equation of the conjugate hyperbola is $\frac{(x+4)^2}{16} - \frac{(y+1)^2}{9} = -1$.Multiplying by $144$: $9(x+4)^2 - 16(y+1)^2 = -144$.$9(x^2 + 8x + 16) - 16(y^2 + 2y + 1) = -144$$9x^2 + 72x + 144 - 16y^2 - 32y - 16 = -144$$9x^2 - 16y^2 + 72x - 32y + 128 = -144$$9x^2 - 16y^2 + 72x - 32y + 272 = 0$.

If the equation of a hyperbola is $9x^2 - 16y^2 + 72x - 32y - 16 = 0$,then the equation of its conjugate hyperbola is

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