A line y=mx+1 meets the circle `(x-3)^(2)+(y+2)^(2)=25` at point P and Q. if mid point of PQ has abscissa of `-(3)/(5)` then value of m satisfies

Options

A. `6 le m lt8`
B. `2 le m lt 4`
C. `-3 le m lt -1`
D. `4 le m lt 6`

Answer

B

Explanation

For point R, `x=-(3)/(5)impliesy=1-(3m)/(5)" "R(-(3)/(5),1-(3m)/(5))`
slope of CR `=(1-(3m)/(5)+2)/(-(3)/(5)-3)=-(1)/(m)implies(15-3m)/(-3-15)=-(1)/(m)`
`15m-3m^(2)=18`
`m^(2)-5m+6=0`
`m=2,3`
`2 le m le 4`