What is the eccentricity 16x^2-25y^2=400 ?

The eccentricity 16x^2-25y^2=400 is (sqrt(41))/5

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eccentricity 16x^2-25y^2=400

eccentricity

16 x^{2} - 25 y^{2} = 400

\frac{41}{5}

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - 25 y^{2} = 400 :

Right-left Hyperbola with

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

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

Refine

= \frac{41}{5}

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

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0

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

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

What is the eccentricity 16x^2-25y^2=400 ?
The eccentricity 16x^2-25y^2=400 is (sqrt(41))/5