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

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

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4x^2-4y^2=2y

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{y ^{2}}{5} - \frac{x ^{2}}{4} = 1

\frac{y ^{2}}{4} - \frac{x ^{2}}{32} = 1

3 x^{2} - 4 y^{2} = 12

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

x^{2} - 10 x - 4 y^{2} - 8 y + 17 = 0

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