If ϕ∈0,2π is the eccentric angle of a point on the ellipse x2+3y2=6 at a distance 2 unit from origin , then sum of the values of ϕ is 2020πkthen k=
Given ellipse is x26+y22=1---i
a point on the ellipse (i) is (6cosϕ,2sinϕ)
Since, its distance from the origin is 2
∴ 6cos2ϕ+2sin2ϕ=(2)2⇒4cos2ϕ+2=4⇒4cos2ϕ=2⇒cos2ϕ=1/2⇒2cos2ϕ=1cos2ϕ=0⇒2ϕ=(2n+1)π2;n∈I or ϕ=(2n+1)π/4;n∈I⇒ϕ=π4,3π4,5π4,7π4