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AP EAMCET201921 Apr 2019Evening ShiftMathematicsParabolaActual

The equation of the normal to the parabola y 2 = 4 x which is perpendicular to x + 3 y + 1 = 0 is

Options

  1. A3 x - y = 33
  2. B3 x - y + 33 = 0
  3. C3 x + y = 33
  4. D3 x + y + 33 = 0

Correct answer

A. 3 x - y = 33

Step-by-step solution

The equation of the parabola,  y 2 = 4 x The equation of the normal to the parabola,  y 2 = 4 a x  at  a m 2 , - 2 a m  is  y = m x - 2 a m - a m 3 Here,  a = 1 ,  the equation of the normal becomes,  y = m x - 2 m - m 3   … I Since the normal is perpendicular to the line,  x + 3   y + 1 = 0 Thus,  m 1 m 2 = - 1 m - 1 3 = - 1 m = 3 Substitute the values in equation   I . y = 3 x - 2 3 - 3 3 y = 3 x - 6 - 27 3 x - y = 33

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