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The length of the chord of the ellipse x 2 25 + y 2 16 = 1 , whose mid point is 1 , 2 5 , is equal to:

Options

  1. A1691 5
  2. B2009 5
  3. C1741 5
  4. D1541 5

Correct answer

A. 1691 5

Step-by-step solution

Equation of chord with given middle point is given by, T = S 1 ⇒ x 25 + y 40 = 1 25 + 1 100 ⇒ 8 x + 5 y 200 = 8 + 2 200 ⇒ y = 10 - 8 x 5 . . i ⇒ x 2 25 + ( 10 - 8 x ) 2 400 = 1 ⇒ 16 x 2 + 100 + 64 x 2 - 160 x 400 = 1 ⇒ 4 x 2 - 8 x - 15 = 0 ⇒ x = 8 ± 304 8 ⇒ x 1 = 8 + 304 8 ; x 2 = 8 - 304 8 Similarly, y = 10 - 8 ± 304 5 = 2 ± 304 5 ⇒ y 1 = 2 - 304 5 ; y 2 = 2 + 304 5 Distance = x 1 - x 2 2 + y 1 - y 2 2 = 4 × 304 64 + 4 × 304 25 = 1691 5

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