Find the equation of an ellipse whose axes lie along the coordinate axes, which passes through the point (-3,1) and has eccentricity equal to `sqrt(2//5)`

Explanation

Let the equation of the ellipse be `x^2/a^2+y^2/b^2=1`

It passes through the point `(-3,1)`.

`therefore 9/a^2+1/b^2=1`

and `e=sqrt2/5`

Now, `b^2=a^2(1-e^2)`

`Rightarrow b^2=a^2(1-2/5)`

`Rightarrow b^2=a^2 times 3/5 or (3a^2)/5`

Substituting the value of `b^2` in eq. (2), we get:

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