What is 9x^2-36x-16y^2-32y=124 ?

The solution to 9x^2-36x-16y^2-32y=124 is Hyperbola with (h,k)=(2,-1),a=4,b=3

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9x^2-36x-16y^2-32y=124

9 x^{2} - 36 x - 16 y^{2} - 32 y = 124

(h, k) = (2, - 1), a = 4, b = 3

Solution steps

9 x^{2} - 36 x - 16 y^{2} - 32 y = 124

Rewrite

9 x^{2} - 36 x - 16 y^{2} - 32 y = 124

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 1), a = 4, b = 3

4 x^{2} - y^{2} - 36 = 0

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

5 x^{2} - 4 y^{2} - 40 x + 24 y + 24 = 0

4 x^{2} = y^{2} + 4

\frac{( y + 3 ) ^{2}}{9} - \frac{x ^{2}}{16} = 1

What is 9x^2-36x-16y^2-32y=124 ?
The solution to 9x^2-36x-16y^2-32y=124 is Hyperbola with (h,k)=(2,-1),a=4,b=3