What is 4x^2-9y^2-16x-36y-56=0 ?

The solution to 4x^2-9y^2-16x-36y-56=0 is Hyperbola with (h,k)=(2,-2),a=3,b=2

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4x^2-9y^2-16x-36y-56=0

4 x^{2} - 9 y^{2} - 16 x - 36 y - 56 = 0

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

Solution steps

4 x^{2} - 9 y^{2} - 16 x - 36 y - 56 = 0

Rewrite

4 x^{2} - 9 y^{2} - 16 x - 36 y - 56 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(x - 5)^{2} - 3 (y + 2)^{2} = 4

\frac{y ^{2}}{8} - \frac{x ^{2}}{5} = 1

7 x^{2} - 24 y^{2} = 41

9 y^{2} - 4 x^{2} - 36 y - 8 x = 4

- x^{2} + y^{2} - 8 y - 9 = 0

What is 4x^2-9y^2-16x-36y-56=0 ?
The solution to 4x^2-9y^2-16x-36y-56=0 is Hyperbola with (h,k)=(2,-2),a=3,b=2