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

The solution to y^2-4x^2-12y-16x+16=0 is Hyperbola with (h,k)=(-2,6),a=2,b=1

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

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

(h, k) = (- 2, 6), a = 2, b = 1

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 6 ) ^{2}}{2 ^{2}} - \frac{( x - ( - 2 ) ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, 6), a = 2, b = 1

26 x^{2} - 17 y^{2} = 284

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

\frac{( x - 3 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{12} = 1

4 x^{2} - 9 y^{2} - 16 x + 18 y + 11 = 0

\frac{( y + 1 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{4} = 1

What is y^2-4x^2-12y-16x+16=0 ?
The solution to y^2-4x^2-12y-16x+16=0 is Hyperbola with (h,k)=(-2,6),a=2,b=1