What is y^2+2y=4x^2+3 ?

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

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y^2+2y=4x^2+3

y^{2} + 2 y = 4 x^{2} + 3

(h, k) = (0, - 1), a = 2, b = 1

Solution steps

y^{2} + 2 y = 4 x^{2} + 3

Rewrite

y^{2} + 2 y = 4 x^{2} + 3

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 2, b = 1

10 y^{2} - 9 x^{2} = 80

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

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

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

9 x^{2} - 16 y^{2} - 18 x + 64 y - 199 = 0

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