What is the eccentricity 4x^2+5y^2=20 ?

The eccentricity 4x^2+5y^2=20 is 1/(sqrt(5))

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eccentricity 4x^2+5y^2=20

eccentricity

4 x^{2} + 5 y^{2} = 20

\frac{1}{5}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 5 y^{2} = 20 :

Ellipse with center

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

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

\frac{( 5 ) ^{2} - 2 ^{2}}{5} = \frac{1}{5}

= \frac{1}{5}

x^{2} + y^{2} - 2 y = 0

6 x^{2} - 12 x + 54 y^{2} + 108 y - 426 = 0

\frac{( x - 4 ) ^{2}}{4} + \frac{y ^{2}}{16} = 1

6 x^{2} + 9 y^{2} = 54

10 x^{2} + 35 y^{2} = 5

What is the eccentricity 4x^2+5y^2=20 ?
The eccentricity 4x^2+5y^2=20 is 1/(sqrt(5))