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

\frac{x ^{2}}{36} - \frac{y ^{2}}{13} = 1

\frac{x ^{2}}{36} - \frac{y ^{2}}{25} = 1

y^{2} - 4 y - 4 x^{2} + 13 = 0

16 y^{2} - x^{2} = 144

\frac{x ^{2}}{5} - \frac{y ^{2}}{9} = 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