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Question

y2=4x and y2=8(xa) intersect at point A and C. Points O(0,0), A, B(a,0), C are concyclic.

The length of common chord of parabolas is

A
26
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B
43
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C
65
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D
82
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Solution

The correct option is D 82
Solving the given parabolas, we have
8(xa)=4x
x=2a3
Therefore, the points of intersection are (2a3,±8a3)
Now, OABC is noncyclic.

Hence, OAB must be a right angle. So,
Slope of OA×Slope of AB=1
8a32a3×8a3a(2a3)=1
a=12
Therefore, the coordinates of A and C are (8,42) and (8,42) respectively.
So, Length of common chord =82


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