What is 9x^2-36x-4y^2-24y-36=0 ?

The solution to 9x^2-36x-4y^2-24y-36=0 is Hyperbola with (h,k)=(2,-3),a=2,b=3

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9x^2-36x-4y^2-24y-36=0

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

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

Solution steps

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

Rewrite

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} + 4 y^{2} = 16

4 x^{2} + 3 y^{2} + 8 x - 24 y + 51 = 0

9 y^{2} - 25 x^{2} = 225

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

\frac{x ^{2}}{81} + \frac{y ^{2}}{9} = 1

What is 9x^2-36x-4y^2-24y-36=0 ?
The solution to 9x^2-36x-4y^2-24y-36=0 is Hyperbola with (h,k)=(2,-3),a=2,b=3