What is the eccentricity (y^2)/4-(x+1)^2=1 ?

The eccentricity (y^2)/4-(x+1)^2=1 is (sqrt(5))/2

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eccentricity (y^2)/4-(x+1)^2=1

eccentricity

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

\frac{5}{2}

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (- 1, 0), a = 2, b = 1

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

Refine

= \frac{5}{2}

3 x^{2} - 4 y^{2} = 12

4 y^{2} - 9 x^{2} + 8 y - 54 x - 113 = 0

\frac{x ^{2}}{36} - \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{40} - \frac{y ^{2}}{120} = 1

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

What is the eccentricity (y^2)/4-(x+1)^2=1 ?
The eccentricity (y^2)/4-(x+1)^2=1 is (sqrt(5))/2