What is x^2-y^2+8y-12=0 ?

The solution to x^2-y^2+8y-12=0 is Hyperbola with (h,k)=(0,4),a=2,b=2

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x^2-y^2+8y-12=0

x^{2} - y^{2} + 8 y - 12 = 0

(h, k) = (0, 4), a = 2, b = 2

Solution steps

x^{2} - y^{2} + 8 y - 12 = 0

Rewrite

x^{2} - y^{2} + 8 y - 12 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 4), a = 2, b = 2

4 x^{2} - 5 y^{2} = 20

x^{2} + (x + 3)^{2} = y^{2}

4 x^{2} - 34 y - 5 y^{2} - 36 = 0

(\frac{2 y - 3 x}{18}) (\frac{2 y + 3 x}{2}) = 1

x^{2} - 2 y^{2} = 7

What is x^2-y^2+8y-12=0 ?
The solution to x^2-y^2+8y-12=0 is Hyperbola with (h,k)=(0,4),a=2,b=2