What is x^2-y^2-10x-10y-1=0 ?

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

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x^2-y^2-10x-10y-1=0

x^{2} - y^{2} - 10 x - 10 y - 1 = 0

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

Solution steps

x^{2} - y^{2} - 10 x - 10 y - 1 = 0

Rewrite

x^{2} - y^{2} - 10 x - 10 y - 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - x - y - 1 = y^{2} - y - x - 3

9 x^{2} = 4 y^{2} - 12

9 y^{2} - 16 x^{2} - 36 y + 32 x - 124 = 0

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

- 25 x^{2} + 100 y^{2} + 10 x - 80 y = - 95

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