What is 9x^2-16y^2-36x-96y-252=0 ?

The solution to 9x^2-16y^2-36x-96y-252=0 is Hyperbola with (h,k)=(2,-3),a=4,b=3

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9x^2-16y^2-36x-96y-252=0

9 x^{2} - 16 y^{2} - 36 x - 96 y - 252 = 0

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

Solution steps

9 x^{2} - 16 y^{2} - 36 x - 96 y - 252 = 0

Rewrite

9 x^{2} - 16 y^{2} - 36 x - 96 y - 252 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y^{2} = 4 x^{2} - 9

\frac{y ^{2}}{121} - \frac{x ^{2}}{196} = 1

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

4 x^{2} - 18 y^{2} = 36

9 x^{2} - 4 y^{2} - 90 x + 32 y - 163 = 0

What is 9x^2-16y^2-36x-96y-252=0 ?
The solution to 9x^2-16y^2-36x-96y-252=0 is Hyperbola with (h,k)=(2,-3),a=4,b=3