What is x^2+12=y^2+6x-2y ?

The solution to x^2+12=y^2+6x-2y is Hyperbola with (h,k)=(3,1),a=2,b=2

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x^2+12=y^2+6x-2y

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

- 36 x^{2} + 25 y^{2} = 900

\frac{y ^{2}}{12} - \frac{x ^{2}}{4} = 1

\frac{16 y ^{2}}{1} - \frac{25 x ^{2}}{1} = 1

- 9 x^{2} + 25 y^{2} - 72 x - 144 - 100 y = 0

\frac{( y - 5 ) ^{2}}{25} - (x - 2)^{2} = 1

What is x^2+12=y^2+6x-2y ?
The solution to x^2+12=y^2+6x-2y is Hyperbola with (h,k)=(3,1),a=2,b=2