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MHT CET202527 Apr 2025Evening ShiftMathematicsParabolaActual

The length of latus rectum of the parabola whose focus is (3,3) and directrix is 3 x-4 y-2=0 is ______ units.

Options

  1. A8
  2. B6
  3. C1 2
  4. D2

Correct answer

A. 8

Step-by-step solution

Finding the latus rectum length requires determining the focus-to-directrix distance. Given focus S(3, 3) and directrix 3x - 4y - 2 = 0 , this distance is calculated as: d = |3(3) - 4(3) - 2| 3^2 + (-4)^2 = 5 5 = 1 For parabolas, the focus-to-directrix distance equals 2a , where a represents the focal length. Thus 2a = 1 . The latus rectum length is given by 4a = 2 (2a) = 2 1 = 2 units. Comparing with the options, the correct choice is D .

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