What is the eccentricity 16x^2-25y^2=100 ?

The eccentricity 16x^2-25y^2=100 is (sqrt(41))/5

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eccentricity 16x^2-25y^2=100

eccentricity

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

\frac{41}{5}

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - 25 y^{2} = 100 :

Right-left Hyperbola with

(h, k) = (0, 0), a = \frac{5}{2}, b = 2

= \frac{( \frac{5}{2} ) ^{2} + 2 ^{2}}{\frac{5}{2}}

Refine

= \frac{41}{5}

9 (y - 2)^{2} - 4 x^{2} = 36

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

9 x^{2} - 9 y^{2} + 18 x + 36 y = 63

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

\frac{( x - 2 ) ^{2}}{9} - (y + 1)^{2} = 1

What is the eccentricity 16x^2-25y^2=100 ?
The eccentricity 16x^2-25y^2=100 is (sqrt(41))/5