What is x^2-y^2-2x+4y-12=0 ?

The solution to x^2-y^2-2x+4y-12=0 is Hyperbola with (h,k)=(1,2),a=3,b=3

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x^2-y^2-2x+4y-12=0

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

36 x^{2} - 4 y^{2} - 36 x - 8 y = 31

\frac{( x - 3 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{9} = 1

9 x^{2} - 4 y^{2} + 54 x + 16 y + 29 = 0

y^{2} - 9 x^{2} = 9

\frac{( y - 0 ) ^{2}}{3 ^{2}} - \frac{( x - 2 ) ^{2}}{4 ^{2}} = 1

What is x^2-y^2-2x+4y-12=0 ?
The solution to x^2-y^2-2x+4y-12=0 is Hyperbola with (h,k)=(1,2),a=3,b=3