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The eccentric angle of a point on the el...

The eccentric angle of a point on the ellipse `(x^2)/4+(y^2)/3=1` at a distance of 5/4 units from the focus on the positive x-axis is `cos^(-1)(3/4)` (b) `pi-cos^(-1)(3/4)` `pi+cos^(-1)(3/4)` (d) none of these

A

`cos^(-1)(3//4)`

B

`cos^(-1)(4//5)`

C

`cos^(-1)(3//5)`

D

none of these

Text Solution

Verified by Experts

Any point on the ellipse is `(2cos theta, sqrt(3) sin theta)`
The focus on the positive x-axis is (1,0)
Given that
`(2 cos theta-1)^(2)+3sin^(2)theta=(25)/(16)`
or `cos theta=(3)/(4)`
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