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NTA Abhyas JEE Main2020MathematicsCirclePractice

Let C 1 : x 2 + y 2 = 5 and C 2 : x 2 + y 2 = 9 . The tangent at ( 1 , 2 ) to C 1 meets the circle C 2 at A and B . The tangents drawn at A and B to circle C 2 meet at T . Then the coordinates of T are

Options

  1. A4 , − 5
  2. B3 5 , 6 5
  3. C4 , 5
  4. D9 5 , 18 5

Correct answer

D. 9 5 , 18 5

Step-by-step solution

Equation of tangent at 1 , 2 to C 1 is x + 2 y − 5 = 0 …(1) Let point T is h , k ∴ Equation of chord of contact w.r.t. C 2 is x h + y k −9 = 0 …(2) ⇒ h 1 = k 2 = 9 5 ⇒ h = 9 5 , k = 18 5

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