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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

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

x^{2} - y^{2} + 6 x - 4 y - 4 = 0

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

16 x^{2} - 9 y^{2} - 96 x + 288 = 0

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