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NTA Abhyas JEE Main2020MathematicsParabolaPractice

The normal to the parabola y 2 = 4 x at P 9 , 6 meets the parabola again at Q . If the tangent at Q meets the directrix at R , then the slope of another tangent drawn from point R to this parabola is

Options

  1. A11
  2. B11 3
  3. C3 11
  4. D3

Correct answer

B. 11 3

Step-by-step solution

Parameter corresponding to P is t 1 = 3 Hence, the parameter corresponding to Q is t 2 = - t 1 - 2 t 1 = - 3 - 2 3 = - 11 3 Let, S t 3 be the point where another tangent from R touches the parabola Now, if the tangent at Q t 2 and S t 3 meet on the directrix at R then t 2 t 3 = - 1 ⇒ t 3 = 3 11 So the equation of the tangent at S is 3 11 y = x + 9 121 Hence, the slope of the tangent at S is 11 3

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