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

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

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

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

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

Solution steps

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

Rewrite

4 x^{2} - y^{2} - 8 x - 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

\frac{y ^{2}}{2} - \frac{x ^{2}}{\frac{8}{7}} = 1

4 x^{2} - y^{2} - 4 x + 3 y - 26 = 0

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

- 9 x^{2} + 4 y^{2} - 144 = 0

\frac{( x - 1 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

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