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Question

If two distinct chords, drawn from the point (p,q) on the circle x2+y2=px+qy, (where pq0) are bisected by the x-axis, then

A
p2=q2
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B
p2=8q2
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C
p2<8q2
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D
p2>8q2
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Solution

The correct option is D p2>8q2
Let PQ be a chord of the given circle passing through P(p,q) and the coordinates of Q be (x.y) Since PQ is bisected by the x-axis, the mid-point of PQ lies on the x-axis which gives y=q Now Q lies on the circle x2+y2pxqy=0 so x2+q2px+q2=0 so x2+q2px+q2=0 x2px+2q2=0...(i)
which gives two values of x and hence the coordinates of two points Qand R (say). so that the chords PQ and PR are bisected by x-axis. If the chords PQ and PR are distinct, the roots of (i) are real distinct.
the discriminant p28q2>0p2>8q2
350150_196595_ans.jpg

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