What is the eccentricity (y^2)/(25)-(x^2)/(16)=1 ?

The eccentricity (y^2)/(25)-(x^2)/(16)=1 is (sqrt(41))/5

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eccentricity (y^2)/(25)-(x^2)/(16)=1

eccentricity

\frac{y ^{2}}{25} - \frac{x ^{2}}{16} = 1

\frac{41}{5}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{25} - \frac{x ^{2}}{16} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 5, b = 4

= \frac{5 ^{2} + 4 ^{2}}{5}

Refine

= \frac{41}{5}

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

9 x^{2} - 16 y^{2} = 144

\frac{x ^{2}}{100} - \frac{y ^{2}}{64} = 1

9 y^{2} - 49 x^{2} = 441

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

What is the eccentricity (y^2)/(25)-(x^2)/(16)=1 ?
The eccentricity (y^2)/(25)-(x^2)/(16)=1 is (sqrt(41))/5