the eccentric angle of a point on the ellipse x^2/4+y^2/3=1 at a distance of...

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Shravya

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...5/4 units from the focus on the..? 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
 
Parametric Equations of the given ellipse are

x = 2 cos ?, y = ?3. sin ?

where ? is the parameter( eccentric angle ).

Given P is a point such that SP = 5/4,

where focus S ? ( ae, 0 ) ? ( ?(a²-b²), 0 ) ? ( 1, 0 ).

But SP = a ( 1 - e cos ? ).

? 5/4 = a - (ae) cos ?

? 5/4 = (2) - (1) cos ?

? cos ? = 2 - (5/4) = 3/4

? ? = cos ?¹ ( 3/4 ). .......................... Ans.
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