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The locus of the foot of perpendicular drawn from the centre of the ellipse x 2 + 3 y 2 = 6 on any tangent to it is

Options

  1. Ax 2   +   y 2 2 = 6 x 2 + 2 y 2
  2. Bx 2 +   y 2 2 = 6 x 2 - 2 y 2
  3. Cx 2 - y 2 2 = 6 x 2 + 2 y 2
  4. Dx 2 - y 2 2 = 6 x 2 - 2 y 2

Correct answer

A. x 2   +   y 2 2 = 6 x 2 + 2 y 2

Step-by-step solution

The centre of the given ellipse 0 , 0 The general equation of a tangent to the ellipse x 2 a 2 + y 2 b 2 = 1 is y = m x ± a 2 m 2 + b 2                 . . . 1       Given ellipse : x 2 6 + y 2 2 = 1 A perpendicular line from the centre is y = - x m               . . . 2 Eliminating m , from 1 and 2 y = - x y x ±  a 2 x 2 y 2 + b 2 y 2 = - x 2 ± y  a 2 x 2 y 2 + b 2 ∴  x 2 + y 2 = ± a 2

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