What is x^2-2x-4y^2+24y-31=0 ?

The solution to x^2-2x-4y^2+24y-31=0 is Hyperbola with (h,k)=(1,3),a=1,b=2

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x^2-2x-4y^2+24y-31=0

x^{2} - 2 x - 4 y^{2} + 24 y - 31 = 0

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

Solution steps

x^{2} - 2 x - 4 y^{2} + 24 y - 31 = 0

Rewrite

x^{2} - 2 x - 4 y^{2} + 24 y - 31 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

- x^{2} + y^{2} - 6 = 3

x^{2} + 12 x - y^{2} + 10 y = 12

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

y^{2} - 4 y = 3 x^{2} - 10 x

What is x^2-2x-4y^2+24y-31=0 ?
The solution to x^2-2x-4y^2+24y-31=0 is Hyperbola with (h,k)=(1,3),a=1,b=2