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

Question

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

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

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A::C
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.`

6 views Answered 2023-02-05 15:29