What is the eccentricity 16x^2+80y^2=1280 ?

The eccentricity 16x^2+80y^2=1280 is 2/(sqrt(5))

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eccentricity 16x^2+80y^2=1280

eccentricity

16 x^{2} + 80 y^{2} = 1280

\frac{2}{5}

Solution steps

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

Calculate ellipse properties

16 x^{2} + 80 y^{2} = 1280 :

Ellipse with center

(h, k) = (0, 0), a = 45, b = 4

= \frac{( 4 5 ) ^{2} - 4 ^{2}}{4 5}

\frac{( 4 5 ) ^{2} - 4 ^{2}}{4 5} = \frac{2}{5}

= \frac{2}{5}

x^{2} + 9 y^{2} = 9

4 x^{2} + 9 y^{2} = 13

4 - x^{2} - 4 y^{2} > 0

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

2 x^{2} + y^{2} = 1

What is the eccentricity 16x^2+80y^2=1280 ?
The eccentricity 16x^2+80y^2=1280 is 2/(sqrt(5))