What is x^2-y^2-8x-8y-15=0 ?

The solution to x^2-y^2-8x-8y-15=0 is Hyperbola with (h,k)=(4,-4),a=sqrt(15),b=sqrt(15)

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x^2-y^2-8x-8y-15=0

x^{2} - y^{2} - 8 x - 8 y - 15 = 0

(h, k) = (4, - 4), a = 15, b = 15

Solution steps

x^{2} - y^{2} - 8 x - 8 y - 15 = 0

Rewrite

x^{2} - y^{2} - 8 x - 8 y - 15 = 0

in the form of a standard hyperbola equation

\frac{( x - 4 ) ^{2}}{( 15 ) ^{2}} - \frac{( y - ( - 4 ) ) ^{2}}{( 15 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, - 4), a = 15, b = 15

\frac{a + 10}{b} = \frac{b}{a}

(x - 2)^{2} - (y + 5)^{2} = 18

\frac{4 y ^{2}}{9} - \frac{4 x ^{2}}{27} = 1

2 x^{2} - 3 y^{2} + 8 x + 6 y - 115 = 0

x^{2} - 4 y^{2} = 5

What is x^2-y^2-8x-8y-15=0 ?
The solution to x^2-y^2-8x-8y-15=0 is Hyperbola with (h,k)=(4,-4),a=sqrt(15),b=sqrt(15)