A line y=mx+1 intersects the circle (x-3)^2+(y+2)^2=25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate - 3 5 , then which one of the following options is correct?

JEE Advanced 2019 Mathematics question

A line intersects the circle at the points and . If the midpoint of the line segment has -coordinate , then which one of the following options is correct?

(A)
(B)Correct
(C)
(D)

Answer: (B)

Solution

The midpoint is . The line joining the centre to the midpoint of a chord is perpendicular to the chord: slope of

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Question ID VK-026846