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MHT CET2012MathematicsParabola

The pole of the line L x+m y+n=0 w.r.t. the parabola y²=4 a x will be

Options

  1. A( -n l , -2 a m l )
  2. B( -n l , 2 a m l )
  3. C( n l , -2 a m l )
  4. D( n l , 2 a m l )

Correct answer

C. ( n l , -2 a m l )

Step-by-step solution

Tangent of the parabola y²=4 a x at point P (x₁, y₁ ) is y y₁=2 a (x+x₁ ) 2 a x₁-y y₁+2 x=0 ( i ) which is also equation of the polar of the parabola y²=4 a x . Same as the line b x+m y+n=0...(ii) On comparing both lines, we get 2 a l = -y m = 2 a x n Taking first two parts (y=- 2 a m l ) Taking first and last parts, (x= n l ) Required pole of the line is n l , -2 a m l .

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