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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

2 x^{2} - 4 y^{2} + 8 x - 12 y + 64 = 0

4 x^{2} - y^{2} - 2 y - 5 = 0

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

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

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