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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} + 2 x - y^{2} - 2 y + 3 = 0

(x - 3)^{2} = 8 + (y + 5)^{2}

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

4 x^{2} + 8 x - 4 y^{2} + 12 y - 3 = 0

\frac{( x + 4 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{36} = 1

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