Question

If P(x₁, y₁) is a point on an ellipse (x²/a²) + (y²/b²) = 1 and it's one focus is S(ae, 0) then PS is equal to .........

(a) a + ex₁

(b) a – ex₁ 

(c) ae + x₁

(d) ae – x₁

Answer 1

The correct option (b) a – ex₁

Explanation:

P(x₁, y₁) is point on ellipse and focus is S(ae, 0).

Let ZM is the directrix of ellipse then 

SP = e ∙ PM and PM = [(a/e) – x₁]

∴  SP = e[(a/e) – x₁]

∴  SP = a – ex₁

i.e.   PS = a – ex₁.