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

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

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

eccentricity

\frac{( x + 1 ) ^{2}}{4} - (y - 5)^{2} = 4

\frac{5}{2}

Solution steps

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

Calculate Hyperbola properties

\frac{( x + 1 ) ^{2}}{4} - (y - 5)^{2} = 4 :

Right-left Hyperbola with

(h, k) = (- 1, 5), a = 4, b = 2

= \frac{4 ^{2} + 2 ^{2}}{4}

Refine

= \frac{5}{2}

9 x^{2} - 16 y^{2} = 144

\frac{x ^{2}}{100} - \frac{y ^{2}}{64} = 1

9 y^{2} - 49 x^{2} = 441

9 x^{2} - 18 x - 16 y^{2} - 64 y = 199

\frac{y ^{2}}{16} - \frac{x ^{2}}{9} = 1

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