What is y^2-4x^2-16x-2y-19=0 ?

The solution to y^2-4x^2-16x-2y-19=0 is Hyperbola with (h,k)=(-2,1),a=2,b=1

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y^2-4x^2-16x-2y-19=0

y^{2} - 4 x^{2} - 16 x - 2 y - 19 = 0

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

Solution steps

y^{2} - 4 x^{2} - 16 x - 2 y - 19 = 0

Rewrite

y^{2} - 4 x^{2} - 16 x - 2 y - 19 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

9 x^{2} - 16 y^{2} + 144 = 0

36 (y + 4)^{2} - 16 (x - 3)^{2} = 576

(x - 2)^{2} - (y + 3)^{2} = 12

4 x^{2} - y^{2} + 12 x + 5 = 0

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

What is y^2-4x^2-16x-2y-19=0 ?
The solution to y^2-4x^2-16x-2y-19=0 is Hyperbola with (h,k)=(-2,1),a=2,b=1