Question

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.

Answer 1

Centre of the given circle is C(0,0) and radius is 1. Distance of centre of the circle from the given line is
`CP=(|m(0)-0+2|)/(sqrt(1+m^(2)))=(2)/(sqrt(1+m^(2)))`
If the line cuts the circle at two distinct or coincident points, then
`CP lt1`
`:. (2)/(sqrt(1+m^(2))) le1`
`implies 1+m^(2)ge4`
`implies m^(2)ge3`
`implies m in(-oo,-sqrt(3)]cup[sqrt(3),oo)`