What is -4x^2+9y^2+24x-36y-32=0 ?

The solution to -4x^2+9y^2+24x-36y-32=0 is Hyperbola with (h,k)=(3,2),a=(4sqrt(2))/3 ,b=2sqrt(2)

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-4x^2+9y^2+24x-36y-32=0

- 4 x^{2} + 9 y^{2} + 24 x - 36 y - 32 = 0

(h, k) = (3, 2), a = \frac{4 2}{3}, b = 22

Solution steps

- 4 x^{2} + 9 y^{2} + 24 x - 36 y - 32 = 0

Rewrite

- 4 x^{2} + 9 y^{2} + 24 x - 36 y - 32 = 0

in the form of a standard hyperbola equation

\frac{( y - 2 ) ^{2}}{( \frac{4 2}{3} ) ^{2}} - \frac{( x - 3 ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 2), a = \frac{4 2}{3}, b = 22

\frac{x ^{2}}{24} - \frac{y ^{2}}{9} = 1

x^{2} - y^{2} - 6 y = 0

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

x^{(2)} - y^{(2)} = 25

x^{(2)} - y^{(2)} = 20

What is -4x^2+9y^2+24x-36y-32=0 ?
The solution to -4x^2+9y^2+24x-36y-32=0 is Hyperbola with (h,k)=(3,2),a=(4sqrt(2))/3 ,b=2sqrt(2)