What is 4x^2-4y^2-2x+8y-4=0 ?

The solution to 4x^2-4y^2-2x+8y-4=0 is Hyperbola with (h,k)=(1/4 ,1),a= 1/4 ,b= 1/4

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4x^2-4y^2-2x+8y-4=0

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

4 x^{2} - 4 y^{2} + 100 = 0

3 x^{(2)} - 6 x - 4 y^{(2)} - 9 = 0

x^{2} - 3 y^{2} - 6 x + 12 = 0

\frac{- y ^{2}}{4} + \frac{z ^{2}}{4} = - \frac{3}{4}

2 x^{2} - y^{2} = 17

What is 4x^2-4y^2-2x+8y-4=0 ?
The solution to 4x^2-4y^2-2x+8y-4=0 is Hyperbola with (h,k)=(1/4 ,1),a= 1/4 ,b= 1/4