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JEE Advanced2010MathematicsParabolaActual

Let A and B be two distinct points on the parabola y^2=4 x . If the axis of the parabola touches a circle of radius r having A B as its diameter, then the slope of the line joining A and B can be

Options

  1. A- 1 r
  2. B1 r
  3. C2 r
  4. D- 2 r

Correct answer

C. 2 r

Step-by-step solution

Here, coordinate M= ( t₁^2+t₂^2 2 , t₁+t₂ ) i e , mid point of chord A B . M P=t₁+t₂=r Also, m_ A B = 2 t₂-2 t₁ t₂^2-t₁^2 = 2^ (i) t₂+t₁ (when A B is chord) m_ A B = 2 r [from Eq. (i)] Also, m_ A^ B^ =- 2 r (when A^ B^ is chord) Hence, (c, d) is the correct option.

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