What is x^{(2)}-2x-4y^{(2)}+24y=31 ?

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

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

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

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

Solution steps

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

Rewrite

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

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

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

y^{2} - 4 y - 4 x^{2} + 8 x = 4

\frac{1}{144} x^{2} - \frac{1}{196} y^{2} = 1

\frac{x ^{2}}{5 0 ^{2}} - \frac{y ^{2}}{2 5 ^{2}} = 1

81 x^{2} - 64 y^{2} + 1134 x - 640 y - 2815 = 0

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