Find the equations of lines passing through the point `(1,0)` and a distance `(sqrt(3))/2` from the origin.

Options

A. `sqrt3x+y-sqrt3=0,sqrt3x-y-sqrt3=0`
B. `sqrt3x+y+sqrt3=0,sqrt3x-y+sqrt3=0`
C. `x+sqrt3y-sqrt3=0,x-sqrt3y-sqrt3=0`
D. None of the above

Answer

A

Explanation

Let slope of the line be m.
`because ` Equation of line passing through (1,0) is `y-0=m(x-1)`
`rArry-mx+m=0`
Since, the distance from origin is `sqrt(3)/(2)`.
Then , `sqrt(3)/(2)=(0-0+m)/(sqrt(1+m^2))`
`rArr(3)/(4)=(m^(2))/(1+m^2)`
`rArr3+3m^2=4m^2`
`rArr m^2=3`
`rArrm=pmsqrt3`
So, the first equation of line is `y=-sqrt3(x-1)`
`rArrsqrt3x-y-sqrt3=0`
and the second equation of line is `y=-sqrt3(x-1)`
`rArrsqrt3x+y-sqrt3=0`