What is 4y^2+2y=x^2-1 ?

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

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4y^2+2y=x^2-1

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

(h, k) = (0, - \frac{1}{4}), a = \frac{3}{2}, b = \frac{3}{4}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} - \frac{( y - ( - \frac{1}{4} ) ) ^{2}}{( \frac{3}{4} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - \frac{1}{4}), a = \frac{3}{2}, b = \frac{3}{4}

9 x^{2} - 4 y^{2} - 18 x - 24 y - 63 = 0

9 x^{2} - 4 y^{2} + 54 x - 8 y + 78 = 0

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

8 x^{2} - 3 y^{2} = 120

5 y^{2} - 16 x^{2} + 400 = 0

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