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AP EAMCET2013MathematicsParabola

A circle of radius 4 , drawn on a chord of the parabola y^2=8 x as diameter, touches the axis of the parabola. Then, the slope of the chord is

Options

  1. A1 2
  2. B3 4
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

Given, equation of parabola is aligned y^2 & =8 x a & =2 aligned Let (h, 4) be the coordinate of mid-point of chord. Then, equation of chord is y-4=m(x-h) If line (ii) passes through the point P (2 t₁^2, 4 t₁ ) and Q (2 t₂^2, 4 t₂ ) on parabola Eq. (i), then y (t₁+t₂ )-2 x-4 t_ t₂ =0 having slope m= 2 t₁+t₂ Since, (h, 4) is the mid-point of P Q . Therefore, aligned & 2 4=4 (t₁+t₂ ) & t₁+t₂=2 aligned Hence, slope of chord P Q is m= 2 2 =1 [using Eq. (iv)]

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