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AP EAMCET2005MathematicsParabola

The line among the following which touches the parabola y^2=4 a x , is

Options

  1. Ax+m y+a m^3=0
  2. Bx-m y+a m^2=0
  3. Cx+m y-a m^2=0
  4. Dy+m x+a m^2=0

Correct answer

B. x-m y+a m^2=0

Step-by-step solution

Given equation of parabola is y^2=4 a x Let the equation of line be y=m x+c If this line touches the parabola, then aligned & c= a m & y=m x+ a m m y=m^2 x+a & replacing m by 1 m , we get & m y=x+a m^2 & x-m y+a m^2=0 aligned

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