What is 4y^2-2x^2-4y-15=0 ?

The solution to 4y^2-2x^2-4y-15=0 is Hyperbola with (h,k)=(0, 1/2),a=2,b=2sqrt(2)

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4y^2-2x^2-4y-15=0

4 y^{2} - 2 x^{2} - 4 y - 15 = 0

(h, k) = (0, \frac{1}{2}), a = 2, b = 22

Solution steps

4 y^{2} - 2 x^{2} - 4 y - 15 = 0

Rewrite

4 y^{2} - 2 x^{2} - 4 y - 15 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, \frac{1}{2}), a = 2, b = 22

\frac{x ^{2}}{2} - \frac{1}{2} = \frac{y ^{2}}{200} - \frac{1}{200}

- y^{2} + 8 z^{2} = - 8

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

\frac{( x + 8 ) ^{2}}{169} - \frac{( y + 9 ) ^{2}}{25} = 1

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

What is 4y^2-2x^2-4y-15=0 ?
The solution to 4y^2-2x^2-4y-15=0 is Hyperbola with (h,k)=(0, 1/2),a=2,b=2sqrt(2)