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KCET2010MathematicsParabola

The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola x²=-8 y is

Options

  1. Ax =2
  2. Bx=-2
  3. Cy =2
  4. Dy=-2

Correct answer

C. y =2

Step-by-step solution

Given that, parabola x ²=-8 y Here, on comparing with x ²=4 ay 4 a =-8 a =-2 Let the parametric coordinate of parabola x ²=-8 y is, P (4 t ,-2 t ² ) and the other coordinate of latusrectum is P ^ ( -4 t , -2 t ² ) Now, the equation tangent of parabola x²=-8 y At P aligned x x ₁ &=-4 ( y + y ₁ ) ...(i) x (4 t ) &=-4 ( y -2 t ² ) x t &=- y +2 t ² xt &+ y =2 t ² ...(ii) aligned At P ^ x ( -4 t )=-4 ( y - 2 t ² ) x t =y- 2 t² x t= yt ²-2 xt - yt ²=-2 ...(iii) On solving Eqs. (i) and (ii) aligned xt ³+ yt ² &=2 t ⁴ xt -

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