What is 16x^2-9y^2-96x+36y-36=0 ?

The solution to 16x^2-9y^2-96x+36y-36=0 is Hyperbola with (h,k)=(3,2),a=3,b=4

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16x^2-9y^2-96x+36y-36=0

16 x^{2} - 9 y^{2} - 96 x + 36 y - 36 = 0

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

Solution steps

16 x^{2} - 9 y^{2} - 96 x + 36 y - 36 = 0

Rewrite

16 x^{2} - 9 y^{2} - 96 x + 36 y - 36 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

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

\frac{x ^{2}}{1 8 ^{2}} - \frac{y ^{2}}{3 5 ^{2}} = 1

x^{2} - 4 y^{2} - 2 x - 8 y + 1 = 0

\frac{( y - 5 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{12} = 1

What is 16x^2-9y^2-96x+36y-36=0 ?
The solution to 16x^2-9y^2-96x+36y-36=0 is Hyperbola with (h,k)=(3,2),a=3,b=4