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Question:

A line y=mx+1 intersects the circle (x-3)²+(y+2)²=25 at 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?

2≤m<4

4≤m<6

-3≤m<-1

6≤m<8

Solution:

Correct option is B. 2≤m<4
For point R, x=-3/5 ⇒y=1-3m/5
R(-3/5, 1-3m/5)
Slope of CR = (1-3m/5+2)/(-3/5-3) = -1/m
⇒(15-3m-15)/(-18) = -1/m
15m-3m²=18
3m²-15m+18=0
m²-5m+6=0
m=2,3
2≤m≤4.