What is 9y^2-4x^2-18y+24x-63=0 ?

The solution to 9y^2-4x^2-18y+24x-63=0 is Hyperbola with (h,k)=(3,1),a=2,b=3

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9y^2-4x^2-18y+24x-63=0

9 y^{2} - 4 x^{2} - 18 y + 24 x - 63 = 0

(h, k) = (3, 1), a = 2, b = 3

Solution steps

9 y^{2} - 4 x^{2} - 18 y + 24 x - 63 = 0

Rewrite

9 y^{2} - 4 x^{2} - 18 y + 24 x - 63 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, 1), a = 2, b = 3

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

x^{2} + 4 x + 4 - 9 y^{2} = 5

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 1 ) ^{2}}{9} = 1

4 x^{2} - 3 y^{2} - 12 = 0

2 x^{2} - y^{2} = - 8

What is 9y^2-4x^2-18y+24x-63=0 ?
The solution to 9y^2-4x^2-18y+24x-63=0 is Hyperbola with (h,k)=(3,1),a=2,b=3