The equations of the lines passing through the point (1, 0) and at a distance from the origin, are

Let equation of any line passing through the point (1, 0) is

y – y₁ = m(x – x₁)

⇒ y – 0 = m(x – 1)

⇒ y = mx – m

⇒ mx – y – m = 0 …(i)

Given that distance of the line from origin is

Squaring both sides, we get

⇒ 3(m² + 1) = 4m²

⇒ 3m² + 3 = 4m²

⇒ 4m² – 3m² = 3

⇒ m² = 3

⇒ m = ±√3

Putting the value of m = √3 in eq. (i), we get

√3x – y – √3 = 0

Now, putting the value of m = -√3 in eq. (i), we get

-√3x – y – (-√3) = 0

⇒ -√3x – y + √3 = 0

Hence, the correct option is (a)