Question

The length of the major axis of an ellipse is 20 units and its foci are `(pm 5sqrt3, 0).`
Find the equation of the ellipse.

Answer 1

Correct Answer - `x^(2)/100+y^(2)/25 = 1`
Let the equation of the ellipse be `x^(2)/a^(2) + y^(2)/b^(2) = 1.`
Length of the major axis = ` 20 hArr 2a = 20 hArr a = 10.`
Foci are `(pm c, 0) rArr c = 5 sqrt 3.`
Now, ` c^(2) = (a^(2)-b^(2)) hArr b^(2) = (a^(2)-c^(2)) = (100-75) = 25.`
`:. ` the required equation is `x^(2)/100+ y^(2)/25 = 1.`