What is x^2-y^2-6x-2y-10=0 ?

The solution to x^2-y^2-6x-2y-10=0 is Hyperbola with (h,k)=(3,-1),a=3sqrt(2),b=3sqrt(2)

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x^2-y^2-6x-2y-10=0

x^{2} - y^{2} - 6 x - 2 y - 10 = 0

(h, k) = (3, - 1), a = 32, b = 32

Solution steps

x^{2} - y^{2} - 6 x - 2 y - 10 = 0

Rewrite

x^{2} - y^{2} - 6 x - 2 y - 10 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 1), a = 32, b = 32

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

X^{2} - 81 Y^{2} = 81

25 x^{2} - y^{2} - 150 x + 200 = 0

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

x^{2} - 4 y^{2} - 2 x + 16 y - 31 = 0

What is x^2-y^2-6x-2y-10=0 ?
The solution to x^2-y^2-6x-2y-10=0 is Hyperbola with (h,k)=(3,-1),a=3sqrt(2),b=3sqrt(2)