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

The solution to 4x^2-2x-4y^2-4=0 is Hyperbola with (h,k)=(1/4 ,0),a=(sqrt(17))/4 ,b=(sqrt(17))/4

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

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

(h, k) = (\frac{1}{4}, 0), a = \frac{17}{4}, b = \frac{17}{4}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{4} ) ^{2}}{( \frac{17}{4} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{17}{4} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{4}, 0), a = \frac{17}{4}, b = \frac{17}{4}

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

y^{2} - 16 x^{2} + 64 x - 208 = 0

9 x^{2} - 9 y^{2} - 18 x + 54 = 0

y^{2} - 4 x^{2} + 16 x - 2 y = 31

(3 y + 3)^{2} + x = (x - 4)^{2}

What is 4x^2-2x-4y^2-4=0 ?
The solution to 4x^2-2x-4y^2-4=0 is Hyperbola with (h,k)=(1/4 ,0),a=(sqrt(17))/4 ,b=(sqrt(17))/4