The sum of the focal distances from any point of the ellipse 9x2 + 16y

1.	The sum of the focal distances from any point of the ellipse 9x2 + 16y2 = 144 is …(a) 32 (b) 18 (c) 16 (d) 8
Answer» (d) 8 We have, 9x² + 16y² = 144 ⇒ (x²/16) + (y²/9) = 1 (Dividing both sides by 144) Here a² = 16, b² = 9 ⇒ a = 4, b = 3 Length of major axis = 2a = 2(4) = 8 Since the sum of the focal distances from any point on the ellipse is equal to its major axis ∴ Required sum = 8

The sum of the focal distances from any point of the ellipse 9x2 + 16y2 = 144 is …(a) 32 (b) 18 (c) 16 (d) 8

Answer»

(d) 8

We have, 9x² + 16y² = 144

⇒ (x²/16) + (y²/9) = 1 (Dividing both sides by 144)

Here a² = 16, b² = 9 ⇒ a = 4, b = 3

Length of major axis = 2a = 2(4) = 8

Since the sum of the focal distances from any point on the ellipse is equal to its major axis

∴ Required sum = 8