What is 9x^2-72x-16y^2-32y=16 ?

The solution to 9x^2-72x-16y^2-32y=16 is Hyperbola with (h,k)=(4,-1),a=4,b=3

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9x^2-72x-16y^2-32y=16

9 x^{2} - 72 x - 16 y^{2} - 32 y = 16

(h, k) = (4, - 1), a = 4, b = 3

Solution steps

9 x^{2} - 72 x - 16 y^{2} - 32 y = 16

Rewrite

9 x^{2} - 72 x - 16 y^{2} - 32 y = 16

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (4, - 1), a = 4, b = 3

16 x^{2} - y^{2} + 16 y - 128 = 0

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

\frac{( y + 1 ) ^{2}}{5 ^{2}} - \frac{( x - 1 ) ^{2}}{1 ^{2}} = 1

4 x^{2} + 4 (0)^{2} - z^{2} = 4

\frac{( x - 3 ) ^{2}}{36} - \frac{( y - 1 ) ^{2}}{16} = 1

What is 9x^2-72x-16y^2-32y=16 ?
The solution to 9x^2-72x-16y^2-32y=16 is Hyperbola with (h,k)=(4,-1),a=4,b=3