﻿ 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 : Kaysons Education

# 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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## Question

### Solution

Correct option is

p2 > 8q2

Let PQ be a chord of the given circle passing through P(pq) and the coordinates of Q be (xy). Since PQ 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 + y2 – px – qy = 0

So            x2 + q2 – px + q2 = 0

Which gives two values of x and hence the coordinates of two points and R (say), so that the chords PQ and PR are bisected by x-axis. If the chords PQ and PR distinct, the roots of (i) are real distinct.

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