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

(74 x 3 + 53 y 8) (74 x 3 - 53 y 8) = 4916 x 6 - 259 y 16

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

a^{2} - b^{2} = 9

\frac{( x + 4 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{16} = 1

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