The eccentric angle of a point on the ellipse $$x24+y23=1$$ at a distance of $$5/4$$ units from the focus on the positive $$x-$$ axis is

Correct option is 1cos−1⁡(3/4)

Questions

$The eccentric angle of a point on the ellipse \frac{x^{2}}{4} + \frac{y^{2}}{3} = 1 at a distance of 5 / 4 units from the focus on the positive x- axis is$

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cos−1⁡(3/4)

π−cos−1⁡(3/4)

π+cos−1⁡(3/4)

None of these

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detailed solution

Correct option is A

Any point on the ellipse is (2cos⁡θ,3sin⁡θ) . The focus on the positive x -axis is (1,0) . (2cos⁡θ−1)2+3sin2⁡θ=2516or cos⁡θ=34

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The eccentric angle of a point on the ellipse x24+y23=1 at a distance of 5/4 units from the focus on the positive x- axis is

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Ready to Test Your Skills?

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$The eccentric angle of a point on the ellipse \frac{x^{2}}{4} + \frac{y^{2}}{3} = 1 at a distance of 5 / 4 units from the focus on the positive x- axis is$