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Question

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

A
|p|=|q|
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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 A p2>8q2
x2+y2pxqy=0
Let T=S1
αx+oyp2(x+2)q2(y)=α2p2 put (xy)(pq)
pαp2(p+α)q2(q)=α2p2
pαp2pαq2=2α2pα
2α24pα+pα+p2+q2=0
2α23p2+(p2+q2)
D>09p24.2(p2+q2)>0
p2>82

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