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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. |
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Answer» 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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