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If two points are taken on the minor axis of the ellipse x 2 25 + y 2 9 = 1 at the same distance from the centre as the foci, then the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is

Options

  1. A25
  2. B18
  3. C50
  4. D80

Correct answer

C. 50

Step-by-step solution

Given ellipse is x 2 25 + y 2 9 = 1 … 1 e = 1 - 9 25 = 4 5 S 0,5 4 5 = S ( 0,4 ) S ' 0 , - 5 4 5 = S ' ( 0 , - 4 ) Let, the tangent to the ellipse be y = m x + 25 m 2 + 9 where, m is a parameter. Now, the sum of the squares of ⊥ distances on this tangent from the points S and S ' is = m 0 - 4 + 25 m 2 + 9 m 2 + 1 2 + m 0 + 4 + 25 m 2 + 9 m 2 + 1 2 = 2 ( m 2 + 1 ) 4 2 + ( 25 m 2 + 9 ) = 50

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