What is 4x^2-9y^2-36y=72 ?

The solution to 4x^2-9y^2-36y=72 is Hyperbola with (h,k)=(0,-2),a=3,b=2

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4x^2-9y^2-36y=72

4 x^{2} - 9 y^{2} - 36 y = 72

(h, k) = (0, - 2), a = 3, b = 2

Solution steps

4 x^{2} - 9 y^{2} - 36 y = 72

Rewrite

4 x^{2} - 9 y^{2} - 36 y = 72

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} - \frac{( y - ( - 2 ) ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 2), a = 3, b = 2

3 x^{2} + 2 x - 3 y^{2} + 14 y = - 24

x, K (x)^{2} = 4 (128 x + x^{2})

\frac{( x - 1 ) ^{2}}{9} - \frac{( y - 5 ) ^{2}}{16} = 1

9 x^{2} - 16 y^{2} - 18 x - 64 y - 200 = 0

4 x^{2} - 16 y^{2} - 64 y - 128 = 0

What is 4x^2-9y^2-36y=72 ?
The solution to 4x^2-9y^2-36y=72 is Hyperbola with (h,k)=(0,-2),a=3,b=2