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

\frac{x ^{2}}{4} - (\frac{( y + 1 )}{16})^{2} = 1

\frac{x ^{2}}{25} - \frac{y ^{2}}{121} = 1

\frac{( x + 4 ) ^{2}}{25} - \frac{( y - 2 ) ^{2}}{4} = 1

x^{2} - y^{2} - 9 = 3

9 x^{2} - 16 = (4 x + s) (4 x - s)

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