What is the eccentricity 4x^2-25y^2+100y=200 ?

The eccentricity 4x^2-25y^2+100y=200 is (sqrt(29))/5

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eccentricity 4x^2-25y^2+100y=200

eccentricity

4 x^{2} - 25 y^{2} + 100 y = 200

\frac{29}{5}

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 25 y^{2} + 100 y = 200 :

Right-left Hyperbola with

(h, k) = (0, 2), a = 5, b = 2

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

Refine

= \frac{29}{5}

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

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

\frac{y ^{2}}{25} - \frac{x ^{2}}{81} = 1

- x^{2} + 9 y^{2} + 4 x + 54 y + 68 = 0

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0

What is the eccentricity 4x^2-25y^2+100y=200 ?
The eccentricity 4x^2-25y^2+100y=200 is (sqrt(29))/5