What is the eccentricity (x^2)/(100)-(y^2)/(64)=1 ?

The eccentricity (x^2)/(100)-(y^2)/(64)=1 is (sqrt(41))/5

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eccentricity (x^2)/(100)-(y^2)/(64)=1

eccentricity

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

\frac{41}{5}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 10, b = 8

= \frac{1 0 ^{2} + 8 ^{2}}{10}

Refine

= \frac{41}{5}

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

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{9} = 1

x^{2} - y^{2} = 3

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

What is the eccentricity (x^2)/(100)-(y^2)/(64)=1 ?
The eccentricity (x^2)/(100)-(y^2)/(64)=1 is (sqrt(41))/5