Find the equation of the ellipse whose axes are along the coordinate axes, vertices are `(0,+-10)` and eccentricity`e=4//5` .

Explanation

Let the equation of the required ellipse be

`(x^2)/(a^2)​+(y^2)/(b^2)​=1⟶(1)`

and b=10

Now,`a^2=b^2(1−e^2)`

`⇒a^2=100(1−(16)/(25)​)`

`⇒a^2=36`

substituting the value of a^2 and b^2 in equation (1)

we get, `(x^2)/(36)​+(y^2)/(100)​=1`

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