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

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

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

eccentricity

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

\frac{13}{3}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

= \frac{13}{3}

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

\frac{x ^{2}}{45} - \frac{y ^{2}}{216} = 1

16 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

\frac{x ^{2}}{4} - \frac{y ^{2}}{16} = 1

49 x^{2} - 25 y^{2} - 686 x - 50 y + 2375 = 0

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