Question

If S and S' are two foci of an ellipse 16x² + 25y² = 400 and PSQ is a focal chord such that SP = 16 then S'Q = ........

(a) (74/9)

(b) (54/9)

(c) (64/9)

(d) (44/9)

Answer 1

The correct option (a) (74/9)

Explanation:

Ellipse: 16x² + 25y² = 400 ⇒ (x²/25) + (y²/16) = 1

and SP = 16

∵   (1/SP) + (1/SQ) = (2a/b²)

⇒   (1/16) + (1/SQ) = [(2 × 5)/16] = (10/16)

∴   SQ = (16/9)

Now    SQ + SQ' = 2a

∴   SQ + SQ' = 10

∴    SQ' = 10 – (16/9)

∴  SQ' = (74/9).