What is the eccentricity 9(y-2)^2-4x^2=36 ?

The eccentricity 9(y-2)^2-4x^2=36 is (sqrt(13))/2

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eccentricity 9(y-2)^2-4x^2=36

eccentricity

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

\frac{13}{2}

Solution steps

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

Calculate Hyperbola properties

9 (y - 2)^{2} - 4 x^{2} = 36 :

Up-down Hyperbola with

(h, k) = (0, 2), a = 2, b = 3

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

Refine

= \frac{13}{2}

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

9 x^{2} - 9 y^{2} + 18 x + 36 y = 63

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

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

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

What is the eccentricity 9(y-2)^2-4x^2=36 ?
The eccentricity 9(y-2)^2-4x^2=36 is (sqrt(13))/2