What is 9y^2-4x^2-8x-12y+16=0 ?

The solution to 9y^2-4x^2-8x-12y+16=0 is Hyperbola with (h,k)=(-1, 2/3),a=2,b= 4/3

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9y^2-4x^2-8x-12y+16=0

9 y^{2} - 4 x^{2} - 8 x - 12 y + 16 = 0

(h, k) = (- 1, \frac{2}{3}), a = 2, b = \frac{4}{3}

Solution steps

9 y^{2} - 4 x^{2} - 8 x - 12 y + 16 = 0

Rewrite

9 y^{2} - 4 x^{2} - 8 x - 12 y + 16 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, \frac{2}{3}), a = 2, b = \frac{4}{3}

\frac{( x + 2 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{25} = 1

x^{2} - 2 y^{2} = 3

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

x^{2} - 20 x - 4 y^{2} - 64 y - 172 = 0

5 x^{2} - 4 y^{2} = 20

What is 9y^2-4x^2-8x-12y+16=0 ?
The solution to 9y^2-4x^2-8x-12y+16=0 is Hyperbola with (h,k)=(-1, 2/3),a=2,b= 4/3