Find the range of values of `m` for which the line `y=m x+2` cuts the circle `x^2+y^2=1` at distinct or coincident points.

Options

A. `(-oo, -sqrt(3) "]" uu"["sqrt(3), oo)`
B. `[-sqrt(3), sqrt(3)]`
C. `[sqrt(3),oo)`
D. none of these

Answer

A

Explanation

If the line `y=mx+2` cuts the circle `x^(2)+y^(2)=1` at distinct or coincident points, then
Length of the perpendicular from the centre `le` Radius
`rArr |(2)/(sqrt(m^(2)+1))|le 1`
`rArr 4 le m^(2)+1`
`rArr m^(2)-3 le 0`
`rArr (m-sqrt(3))(m+sqrt(3))le0rArr m in (-oo, -sqrt(3)]uu[sqrt(3), oo)`