Given that the latus rectum of an ellipse subtends an right angle with centre of the ellipse. We need to find the eccentricity of the ellipse.

Let us assume that the equation of the ellipse be (a²>b²) such that the centre is O(0,0).

We know that the ends A and B of the latus rectum are .

Let us find the slope(m₁) of the OA.

We know that the slope of the line joining points (x₁,y₁) and (x₂,y₂) is

⇒

⇒

Let us find the slope(m₂) of the OB.

We know that the slope of the line joining points (x₁,y₁) and (x₂,y₂) is

⇒

⇒

We know that the product of the slopes of the perpendicular is - 1.

⇒ m₁.m₂ = - 1

⇒ = - 1

⇒ b⁴ = a⁴e²

⇒

⇒