The number of points on the line 3x + 4y =5, which are at a distance of sec2⁡θ+2cosec2⁡θ,θ∈R  from the point (1, 3) is

The perpendicular distance of (1, 3) from the line 3x + 4y=5 is 2 units whilesec2⁡θ+2cosec2⁡θ≥3 as sec 2θ,cosec2⁡θ≥1So, there will be two such points on the line.