Question

If P(x, y) be any point on 16x² + 25y² = 400 with foci F₁ (3, 0) and F₂ (- 3, 0) then PF₁ + PF₂ is 

(a) 8 

(b) 6 

(c) 10 

(d) 12

Answer 1

(c) 10

F₁P + F₂P = 2a 

Here the equation is 16x² + 25y² = 400

(÷ by 400) ⇒ (16x²/400) + (25y²/400) = 1 

⇒ (x²/25) + (y²/16) = 1

a² = 25 => a = 5 

∴ 2a = 10