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AP EAMCET201920 Apr 2019Morning ShiftMathematicsStraight LinesActual

Variable straight lines (y=m x+c ) make intercepts on the curve (y^2-4 a x=0 ) which subtend a right angle at the origin. Then the point of concurrence of these lines (y=m x+c ) is

Options

  1. A((4 a, 0) )
  2. B((2 a, 0) )
  3. C((-4 a, 0) )
  4. D((-2 a, 0) )

Correct answer

A. ((4 a, 0) )

Step-by-step solution

On homogenisation of the curve (y^2-4 a x=0 ) by line (y=m x+c ), we are getting combined equation of straight lines which subtend a right angle at the origin, so ( aligned y^2-4 a x ( y-m x c ) & =0 c+4 a m & =0 (i) aligned ) On putting the value of ' (c ) ' in the line, we get (y=m(x-4 a) ), represent family of line passes through ((4 a, 0) ). Hence, option (1) is correct.

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