What is the eccentricity (x^2}{25}-\frac{y^2)/9 =1 ?

The eccentricity (x^2}{25}-\frac{y^2)/9 =1 is (sqrt(34))/5

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eccentricity (x^2}{25}-\frac{y^2)/9 =1

eccentricity

\frac{x ^{2}}{25} - \frac{y ^{2}}{9} = 1

\frac{34}{5}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{25} - \frac{y ^{2}}{9} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 5, b = 3

= \frac{5 ^{2} + 3 ^{2}}{5}

Refine

= \frac{34}{5}

\frac{x ^{2}}{40} - \frac{y ^{2}}{174} = 1

9 x^{2} - 4 y^{2} - 36 = 0

\frac{x ^{2}}{49} - \frac{y ^{2}}{16} = 1

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

16 x^{2} - 9 y^{2} + 96 x - 72 y + 144 = 0

What is the eccentricity (x^2}{25}-\frac{y^2)/9 =1 ?
The eccentricity (x^2}{25}-\frac{y^2)/9 =1 is (sqrt(34))/5