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

The solution to x^2-y^2-2x-8y-8=0 is Hyperbola with (h,k)=(1,-4),a=sqrt(7),b=sqrt(7)

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

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

(h, k) = (1, - 4), a = 7, b = 7

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - ( - 4 ) ) ^{2}}{( 7 ) ^{2}} - \frac{( x - 1 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 4), a = 7, b = 7

4 x^{2} - 25 y^{2} - 50 y - 125 = 0

9 x^{2} - 16 y^{2} - 54 x - 64 y + 1 = 0

x^{2} - 4 y^{2} - 4 x + 24 y + 37 = 0

6 x^{2} - y^{2} - 12 x - 6 y + 5 = 0

4 a 2 - 9 b 2 = (2 a 2 + 3 b 2) (2 a 2 - 3 b 2)

What is x^2-y^2-2x-8y-8=0 ?
The solution to x^2-y^2-2x-8y-8=0 is Hyperbola with (h,k)=(1,-4),a=sqrt(7),b=sqrt(7)