What is x^2-y^2-2x-6y-12=0 ?

The solution to x^2-y^2-2x-6y-12=0 is Hyperbola with (h,k)=(1,-3),a=2,b=2

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

16 x^{2} - 9 y^{2} + 96 = 0

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

(\frac{( x - 2 )}{16})^{2} - \frac{( y + 3 ) ^{2}}{1} = 1

(3 x - 3)^{2} - (2 y - 4)^{2} = 43 + 9 + 16

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

What is x^2-y^2-2x-6y-12=0 ?
The solution to x^2-y^2-2x-6y-12=0 is Hyperbola with (h,k)=(1,-3),a=2,b=2