First slide
Ellipse
Question

If ϕ0,2π 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=

Moderate
Solution

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)24cos2ϕ+2=44cos2ϕ=2cos2ϕ=1/22cos2ϕ=1cos2ϕ=02ϕ=(2n+1)π2;nI or  ϕ=(2n+1)π/4;nIϕ=π4,3π4,5π4,7π4

Get Instant Solutions
When in doubt download our app. Now available Google Play Store- Doubts App
Download Now
Doubts App