What is 4x^2-8x-y^2-2y-13=0 ?

The solution to 4x^2-8x-y^2-2y-13=0 is Hyperbola with (h,k)=(1,-1),a=2,b=4

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4x^2-8x-y^2-2y-13=0

4 x^{2} - 8 x - y^{2} - 2 y - 13 = 0

(h, k) = (1, - 1), a = 2, b = 4

Solution steps

4 x^{2} - 8 x - y^{2} - 2 y - 13 = 0

Rewrite

4 x^{2} - 8 x - y^{2} - 2 y - 13 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 1), a = 2, b = 4

3 x^{2} - 2 y^{2} + 24 x + 12 y + 24 = 0

9 x^{2} - 16 y^{2} - 54 x + 64 y - 127 = 0

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

y^{2} = 2 x^{2} - 1

3 y^{2} - 6 x^{2} - 12 = 0

What is 4x^2-8x-y^2-2y-13=0 ?
The solution to 4x^2-8x-y^2-2y-13=0 is Hyperbola with (h,k)=(1,-1),a=2,b=4