What is x^2-y^2-2x-8y-10=0 ?

The solution to x^2-y^2-2x-8y-10=0 is Hyperbola with (h,k)=(1,-4),a=sqrt(5),b=sqrt(5)

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x^2-y^2-2x-8y-10=0

x^{2} - y^{2} - 2 x - 8 y - 10 = 0

(h, k) = (1, - 4), a = 5, b = 5

Solution steps

x^{2} - y^{2} - 2 x - 8 y - 10 = 0

Rewrite

x^{2} - y^{2} - 2 x - 8 y - 10 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 4 ) ) ^{2}}{( 5 ) ^{2}} - \frac{( x - 1 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 4), a = 5, b = 5

y^{2} = x^{2} + 361

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

\frac{( x + 3 ) ^{2}}{49} - \frac{( y - 1 ) ^{2}}{48} = 1

5 x^{2} = 5 y^{2} + 45

- 3 y^{2} - 8 x + 4 x^{2} - 8 = 0

What is x^2-y^2-2x-8y-10=0 ?
The solution to x^2-y^2-2x-8y-10=0 is Hyperbola with (h,k)=(1,-4),a=sqrt(5),b=sqrt(5)