What is 4x^2-9y^2+32x+36y+64=0 ?

The solution to 4x^2-9y^2+32x+36y+64=0 is Hyperbola with (h,k)=(-4,2),a=2,b=3

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4x^2-9y^2+32x+36y+64=0

4 x^{2} - 9 y^{2} + 32 x + 36 y + 64 = 0

(h, k) = (- 4, 2), a = 2, b = 3

Solution steps

4 x^{2} - 9 y^{2} + 32 x + 36 y + 64 = 0

Rewrite

4 x^{2} - 9 y^{2} + 32 x + 36 y + 64 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 4, 2), a = 2, b = 3

4 y^{2} - x^{2} - 12 y - 16 x + 16 = 0

- 4 x^{2} + y^{2} = 16

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

\frac{y ^{2}}{25} - \frac{x ^{2}}{144} = 1

3 x^{2} - y^{2} - 18 x + 4 y + 11 = 0

What is 4x^2-9y^2+32x+36y+64=0 ?
The solution to 4x^2-9y^2+32x+36y+64=0 is Hyperbola with (h,k)=(-4,2),a=2,b=3