Question
If PSQ is the focal chord of the parabola y2 = 8x such that SP = 6. Then the length SQ is-
- 4
- 6
- 3
- None of these
Hint:
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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