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In the parabola y^2=4 a x the length of the latus rectum is 6 units and there is a chord passing through its vertex and the negative end of the latus rectum. Then the equation of the chord is

Options

  1. A2 x+y=0
  2. Bx-2 y=0
  3. Cx+2 y=0
  4. D2 x-y=0

Correct answer

A. 2 x+y=0

Step-by-step solution

The equation of the parabola is y^2 = 4ax . The length of the latus rectum is given as 4a = 6 , which implies a = 6 4 = 3 2 . The coordinates of the vertex are (0, 0) . The endpoints of the latus rectum are (a, 2a) and (a, -2a) . The negative end of the latus rectum is (a, -2a) . Substituting a = 3 2 , the coordinates of the negative end of the latus rectum are ( 3 2 , -2 3 2 ) = ( 3 2 , -3) . The chord passes through the vertex (0, 0) and the point ( 3 2 , -3) . The slope m of this chord is m = -3 - 0 3 2 - 0 = -3

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