A line y = mx + 1 intersects the circlex-32+(y+2)2=25 at the point P and Q If the midpoint ofthe line segment PQ has x-coordinate −3/5 then which one of the following options is correct? 

A line y = mx + 1 intersects the circlex-32+(y+2)2=25 at the point 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? 

  1. A

    6m<8

  2. B

    2m<4

  3. C

    4m<6

  4. D

    3m<1

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    Solution:

    Let M be the midpoint of PQ 

    y=mx+1 y=m(3/5)+1y=13m5

     Coordinates of M

    are 35,13m5

    Let C be the centre of the circle. Since CMPQ

    13m5(2)353m=133m5m=185

    (5m)m=6m25m+6=0(m2)(m3)=0m=2,3

    Thus, 2m<4

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