Maths-
General
Easy

Question

If PSQ is the focal chord of the parabola y2 = 8x such that SP = 6. Then the length SQ is-

  1. 4    
  2. 6    
  3. 3    
  4. None of these    

hintHint:

find the harmonic mean of segment lengths and equate it with half of latus rectum length.

The correct answer is: 3


    3
    y2=8x
    a=2
    We know that the harmonic mean of the lengths (PS,QS) where S is the focus is equal to the half of latus rectum

    2.6.SQ/(6+SQ)=4a/2= 2a= 4
    3SQ=6 + SQ
    SQ=6/2=3
    On solving this we get
    SQ = 3

    the harmonic mean of the lengths (PS,QS) where S is the focus is equal to the half of latus rectum.

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