Question

If P is a point on the ellipse `x^2/16 + y^2/25` = 1 whose foci are S and S′, then PS + PS′ = 8.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Let P(x₁, y₁) be a point on the ellipse.

Foci = (± ae, 0)

Here a² = 25 ⇒ a = 5

b² = 16 ⇒ b = 4

b² = a² (1 – e²)

16 = 25(1 – e²)

⇒ `16/25 = 1- e^2`

⇒ e² = `1 - 16/25`

⇒ e² = `9/25`

∴ e = `3/5`

∴ ae = `5 xx 3/5` = 3

So, the foci are S(3, 0) and S(– 3, 0).

Since PS + PS' = 2a = 2 × 5 = 10.