What is the eccentricity 5x^2+10y^2=50 ?

The eccentricity 5x^2+10y^2=50 is 1/(sqrt(2))

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eccentricity 5x^2+10y^2=50

eccentricity

5 x^{2} + 10 y^{2} = 50

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

5 x^{2} + 10 y^{2} = 50 :

Ellipse with center

(h, k) = (0, 0), a = 10, b = 5

= \frac{( 10 ) ^{2} - ( 5 ) ^{2}}{10}

\frac{( 10 ) ^{2} - ( 5 ) ^{2}}{10} = \frac{1}{2}

= \frac{1}{2}

x^{2} + 4 y^{2} - 2 x - 16 y + 13 = 0

x^{2} = 4 y - 2 y^{2}

\frac{( x - 1 ) ^{2}}{6} + \frac{( y - 3 ) ^{2}}{2} = 1

25 x^{2} + 9 y^{2} - 100 x + 18 y - 116 = 0

\frac{x ^{2}}{16} + \frac{y ^{2}}{36} = 1

What is the eccentricity 5x^2+10y^2=50 ?
The eccentricity 5x^2+10y^2=50 is 1/(sqrt(2))