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A line y=mx+1 meets the circle (x-3)^(2)...

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

A

`6 le m lt8`

B

`2 le m lt 4`

C

`-3 le m lt -1`

D

`4 le m lt 6`

Text Solution

Verified by Experts

The correct Answer is:
B

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`
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Knowledge Check

  • 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 ?

    A
    `6 le m lt 8`
    B
    `-3le m lt -1`
    C
    `4le m lt 6`
    D
    `2le m lt 4`

  • If the line y=mx +1 meets the circle x^(2)+y^(2)+3x=0 in two points equidistant and on opposite sides of x-axis, then

    A
    3m-2=0
    B
    2m+3=0
    C
    3m+2=0
    D
    2m-3=0

  • If the line y=mx , meets the lines x+2y=1 and 2x-y+3=0 at one point only then m=?

    A
    `1`
    B
    `-1`
    C
    `-2`
    D
    None of these

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