What is the eccentricity 3x^2+10y^2=30 ?

The eccentricity 3x^2+10y^2=30 is sqrt(7/10)

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eccentricity 3x^2+10y^2=30

eccentricity

3 x^{2} + 10 y^{2} = 30

\frac{7}{10}

Solution steps

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

Calculate ellipse properties

3 x^{2} + 10 y^{2} = 30 :

Ellipse with center

(h, k) = (0, 0), a = 10, b = 3

= \frac{( 10 ) ^{2} - ( 3 ) ^{2}}{10}

\frac{( 10 ) ^{2} - ( 3 ) ^{2}}{10} = \frac{7}{10}

= \frac{7}{10}

x^{2} + 4 y^{2} = 10

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

2 x^{2} + 8 y^{2} = 16

\frac{x ^{2}}{4} + \frac{y ^{2}}{3.2} = 1

9 x^{2} + 7 y^{2} = 63

What is the eccentricity 3x^2+10y^2=30 ?
The eccentricity 3x^2+10y^2=30 is sqrt(7/10)