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.
Text Solution
Verified by Experts
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)`
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