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

The eccentricity y^2-4x^2+4x-2y-4=0 is (sqrt(5))/2

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

eccentricity

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

\frac{5}{2}

Solution steps

= \frac{a ^{2} + b ^{2}}{a}

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

= \frac{2 ^{2} + 1 ^{2}}{2}

Refine

= \frac{5}{2}

16 x^{2} - 4 y^{2} = 49

16 x^{2} - 25 y^{2} = 64

25 x^{2} - 9 y^{2} = 225

9 x^{2} - 16 y^{2} = 64

\frac{x ^{2}}{45} - \frac{y ^{2}}{360} = 1

What is the eccentricity y^2-4x^2+4x-2y-4=0 ?
The eccentricity y^2-4x^2+4x-2y-4=0 is (sqrt(5))/2