What is x^2-y^2+4x-6y=6 ?

The solution to x^2-y^2+4x-6y=6 is Hyperbola with (h,k)=(-2,-3),a=1,b=1

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x^2-y^2+4x-6y=6

x^{2} - y^{2} + 4 x - 6 y = 6

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

Solution steps

x^{2} - y^{2} + 4 x - 6 y = 6

Rewrite

x^{2} - y^{2} + 4 x - 6 y = 6

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 4 y^{2} - 8 x + 16 y - 36 = 0

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

- 5 x^{2} + 4 y^{2} = 16

x^{2} - 4 y^{2} - 4 x - 8 y - 16 = 0

- 9 x^{2} + 25 y^{2} + 50 y - 200 = 0

What is x^2-y^2+4x-6y=6 ?
The solution to x^2-y^2+4x-6y=6 is Hyperbola with (h,k)=(-2,-3),a=1,b=1