If two distinct chords, drawn from the point (p,q) on the circle x2+y2=px+qy(where pq≠0) are bisected by the x-axis, then

B(-p+2x, -q)(-p+2x)2+(-q)2=p(-p+2x)+q(-q)2p2+2q2-6px+4x2=02x2-3px+p2+q2=0∆>0⇒9p2-4.2(p2+q2)>0⇒P2>8q2

If two distinct chords, drawn from the point (p,q) on the circle x2+y2=px+qy(where pq≠0) are bisected by the x-axis, then

B(-p+2x, -q)(-p+2x)2+(-q)2=p(-p+2x)+q(-q)2p2+2q2-6px+4x2=02x2-3px+p2+q2=0∆>0⇒9p2-4.2(p2+q2)>0⇒P2>8q2

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If two distinct chords, drawn from the point (p,q) on the circle x²+y²=px+qy(where pq $\neq$ 0) are bisected by the x-axis, then

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$p^{2} > 8 q^{2}$

$p^{2} < 8 q^{2}$

$p^{2} = 8 q^{2}$

$p^{2} = q^{2}$

answer is D.

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Detailed Solution

B(-p+2x, -q)
(-p+2x)²+(-q)²
=p(-p+2x)+q(-q)
2p²+2q²-6px+4x²=0
2x²-3px+p²+q²=0
$∆$ >0 $\Rightarrow$ 9p²-4.2(p²+q²)>0
$\Rightarrow$ P²>8q²

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If two distinct chords, drawn from the point (p,q) on the circle x2+y2=px+qy(where pq≠0) are bisected by the x-axis, then

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If two distinct chords, drawn from the point (p,q) on the circle x²+y²=px+qy(where pq $\neq$ 0) are bisected by the x-axis, then