Q.

The equation of set of lines which are at a constant distance of 2 units from the origin andαis angle made by perpendicular from origin is

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a

x+y+2=0

b

x+y+4=0

c

xcosα+ysinα=2

d

xcosα+ysinα=12

answer is C.

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Detailed Solution

If normal to the line makes an  angle α with x-axis, then equation of line isxcosα+ysinα=p, where p is distance of line form origin.Here, p=2So,  the equation of line is xcosα+ysinα=2.
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The equation of set of lines which are at a constant distance of 2 units from the origin andαis angle made by perpendicular from origin is