What is 9y^2-4x^2+32x-36y-64=0 ?

The solution to 9y^2-4x^2+32x-36y-64=0 is Hyperbola with (h,k)=(4,2),a=2,b=3

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9y^2-4x^2+32x-36y-64=0

9 y^{2} - 4 x^{2} + 32 x - 36 y - 64 = 0

(h, k) = (4, 2), a = 2, b = 3

Solution steps

9 y^{2} - 4 x^{2} + 32 x - 36 y - 64 = 0

Rewrite

9 y^{2} - 4 x^{2} + 32 x - 36 y - 64 = 0

in the form of a standard hyperbola equation

\frac{( y - 2 ) ^{2}}{2 ^{2}} - \frac{( x - 4 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, 2), a = 2, b = 3

x^{2} + (2 - y^{2}) = 9

4 x^{2} - y^{2} - 16 x + 2 y + 11 = 0

(\frac{( y + 4 )}{9})^{2} - (\frac{( x - 3 )}{25})^{2} = 1

\frac{( x - 3 ) ^{2}}{25} - \frac{( y - 1 ) ^{2}}{4} = 1

\frac{x ^{2}}{7} - \frac{y ^{2}}{6} = 1

What is 9y^2-4x^2+32x-36y-64=0 ?
The solution to 9y^2-4x^2+32x-36y-64=0 is Hyperbola with (h,k)=(4,2),a=2,b=3