What is the eccentricity (y^2)/9-(x^2)/4 =1 ?

The eccentricity (y^2)/9-(x^2)/4 =1 is (sqrt(13))/3

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eccentricity (y^2)/9-(x^2)/4 =1

eccentricity

\frac{y ^{2}}{9} - \frac{x ^{2}}{4} = 1

\frac{13}{3}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{9} - \frac{x ^{2}}{4} = 1 :

Up-down Hyperbola with

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

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

Refine

= \frac{13}{3}

x^{2} - 4 y^{2} = 16

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

9 x^{2} - 4 y^{2} - 18 x - 16 y - 43 = 0

225 x^{2} - 64 y^{2} = 14400

\frac{x ^{2}}{4} - \frac{y ^{2}}{6} = - 1

What is the eccentricity (y^2)/9-(x^2)/4 =1 ?
The eccentricity (y^2)/9-(x^2)/4 =1 is (sqrt(13))/3