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The line 2 x + y = 3 interesects the ellipse 4 x 2 + y 2 = 5 at two points. The point of intersection of the tangents to the ellipse at these points is

Options

  1. A5 6 , 5 6
  2. B5 3 , 5 6
  3. C5 6 , 5 3
  4. D5 3 , 5 3

Correct answer

C. 5 6 , 5 3

Step-by-step solution

Let the required point be h , k . Now from this point, the equation of chord of contact to the ellipse is T = 0 ⇒ 4 hx + ky = 5 which is same as 2 x + y = 3 ⇒ 4 h 2 = k 1 = 5 3 ⇒ h = 5 6 ,   k = 5 3 ⇒ Point of intersection of the tangents is 5 6 , 5 3

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