The equation of the lines passing through the point `(1,0)` and at a distance `(sqrt(3))/2` from the origin is (a)`sqrt(3)x+y-sqrt(3)` =0 (b) `x+sqrt(3)y-sqrt(3)=0` (c) `sqrt(3)x-y-sqrt(3)=0` (d) `x-sqrt(3)y-sqrt(3)=0`

Options

A. `sqrt(3)x+y-sqrt(3) = 0`
B. `x+sqrt(3)y-sqrt(3) = 0`
C. `sqrt(3)x-y-sqrt(3) = 0`
D. `x-sqrt(3)y-sqrt(3) = 0`

Answer

A, C

Explanation

The equations of lines passing through (1,0) are given by y=m(x-1). Its distance from the origin is `sqrt(3)//2`. Hence,
`|(-m)/(sqrt(1+m^(2)))| = (sqrt(3))/(2) " or "m=+-sqrt(3)`
Hence, the lines are `sqrt(3) x+y-sqrt(3) = 0 and sqrt(3) x-y-sqrt(3)=0.`