Find the equation of an ellipse whose eccentricity is , the latus rectum is 5, and the center is at the origin.

Question

Philoid · Accepted Answer

Let the equation of the required ellipse is

…(i)

Given that

we know that,

We know that,

c² = a² – b²

…(ii)

It is also given that, Latus Rectum = 5 …(iii)

We know that,

Substituting the value of a in eq. (ii), we get

Substituting the value of a² and b² in eq. (i), we get