The least distance from origin to a point on the line y = x + 3 which lies at a distance of 2 units from 0 , 3 is

Step-by-step solution

Let the point be x , y on the line y = x + 3 , Now slope of the line is m = 1 ⇒ θ = 45 ° , Now given point is at 2 unit distance from point 0 , 3 Now by parametric form we get, x - 0 cos θ = y - 3 sin θ = ± 2 ⇒ x - 0 1 2 = y - 3 1 2 = ± 2 as  θ = 45 ° ⇒ x = ± 2   &   y = ± 2 + 3 Now distance from origin is given by D = ± 2 - 0 2 + ± 2 + 3 - 0 2 Taking positive sign we get, D = 13 + 6 2 And taking negative sign we get, D