What is the eccentricity (y^2}{36}-\frac{x^2)/9 =1 ?

The eccentricity (y^2}{36}-\frac{x^2)/9 =1 is (sqrt(5))/2

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eccentricity (y^2}{36}-\frac{x^2)/9 =1

eccentricity

\frac{y ^{2}}{36} - \frac{x ^{2}}{9} = 1

\frac{5}{2}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{36} - \frac{x ^{2}}{9} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 6, b = 3

= \frac{6 ^{2} + 3 ^{2}}{6}

Refine

= \frac{5}{2}

16 x^{2} - 25 y^{2} = 100

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

\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

What is the eccentricity (y^2}{36}-\frac{x^2)/9 =1 ?
The eccentricity (y^2}{36}-\frac{x^2)/9 =1 is (sqrt(5))/2