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} - 9 y^{2} = 9

(x + y) (x - y) = 119

y^{2} - 4 x^{2} - 4 y + 24 x = 48

x^{2} - 4 y^{2} + 2 x - 16 y - 19 = 0

(x^{2} - 4 x) - (y^{2} + 4 y) = 1

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