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

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

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

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

(h, k) = (3, 1), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, 1), a = 2, b = 2

4 x^{2} - 24 x - y^{2} - 2 y = - 31

9 y^{2} - 4 x^{2} + 32 x - 36 y - 64 = 0

x^{2} + (2 - y^{2}) = 9

4 x^{2} - y^{2} - 16 x + 2 y + 11 = 0

(\frac{( y + 4 )}{9})^{2} - (\frac{( x - 3 )}{25})^{2} = 1

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