What is x^2+11=y^2+6x-2y ?

The solution to x^2+11=y^2+6x-2y is Hyperbola with (h,k)=(3,1),a=sqrt(3),b=sqrt(3)

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x^2+11=y^2+6x-2y

x^{2} + 11 = y^{2} + 6 x - 2 y

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

Solution steps

x^{2} + 11 = y^{2} + 6 x - 2 y

Rewrite

x^{2} + 11 = y^{2} + 6 x - 2 y

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

4 x^{2} - 8 y^{2} + 6 x + 12 y - 82 = 0

x^{2} - y^{2} - 3 x + 4 y = 0

(x - y) (x + y + 6) = - 9

\frac{( x - 1 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{16} = 1

x^{2} - y^{2} - 2 x - 6 y - 12 = 0

What is x^2+11=y^2+6x-2y ?
The solution to x^2+11=y^2+6x-2y is Hyperbola with (h,k)=(3,1),a=sqrt(3),b=sqrt(3)