What is x^2-6x-6=y^2+6y+6 ?

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

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x^2-6x-6=y^2+6y+6

x^{2} - 6 x - 6 = y^{2} + 6 y + 6

(h, k) = (3, - 3), a = 23, b = 23

Solution steps

x^{2} - 6 x - 6 = y^{2} + 6 y + 6

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 3), a = 23, b = 23

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

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

- 36 y^{2} + 100 x^{2} - 1600 = 0

\frac{( x - 1 ) ^{2}}{16} - \frac{( y + 6 ) ^{2}}{49} = 1

\frac{( y + 2 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

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