Question

The distance from the foci of P(x₁, y₁) on the ellipse (x²/9) + (y²/25) = 1 is ...........

(a) 4 – (5/4)y₁

(b) 5 – (4/5)y₁

(c) 5 – (4/5)x₁

(d) 4 – (4/5)y₁

Answer 1

The correct option  (b) 5 – (4/5)y₁

Explanation:

ellipse: (x²/9) + (y²/25) = 1 ⇒ a = 3 and b = 5.

Thus a < b.

∴ Major axis is y axis and two foci lie on y axis.

Their co-ordinates are (0, ± be)

Now e = √[1 – (a²/b²)] = √[1 – (9/25)] = (4/5)

∴ Focus distance of a point (x₁, y₁) is given by b – ey₁ = 5 – (4/5)y₁.