What is the eccentricity ((x-2)^2)/9-(y+1)^2=1 ?

The eccentricity ((x-2)^2)/9-(y+1)^2=1 is (sqrt(10))/3

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eccentricity ((x-2)^2)/9-(y+1)^2=1

eccentricity

\frac{( x - 2 ) ^{2}}{9} - (y + 1)^{2} = 1

\frac{10}{3}

Solution steps

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

Calculate Hyperbola properties

\frac{( x - 2 ) ^{2}}{9} - (y + 1)^{2} = 1 :

Right-left Hyperbola with

(h, k) = (2, - 1), a = 3, b = 1

= \frac{3 ^{2} + 1 ^{2}}{3}

Refine

= \frac{10}{3}

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

y^{2} - 4 y - 4 x^{2} + 13 = 0

+ \frac{y ^{2}}{25} - \frac{x ^{2}}{4} = 1

9 y^{2} - 4 x^{2} = 36

25 x^{2} + 56476 x - 25 y^{2} - 3 y = 48838

What is the eccentricity ((x-2)^2)/9-(y+1)^2=1 ?
The eccentricity ((x-2)^2)/9-(y+1)^2=1 is (sqrt(10))/3