First slide

Ellipse

Question

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

Moderate

A

$\cos^{- 1} (3 / 4)$
B

$π - \cos^{- 1} (3 / 4)$
C

$π + \cos^{- 1} (3 / 4)$
D

$None of these$

Solution

$\begin{array}{l} Any point on the ellipse is (2 \cos θ, \sqrt{3} \sin θ) . \\ The focus on the positive x -axis is (1, 0) . \end{array}$
$\begin{aligned} (2 \cos θ - 1)^{2} + 3 \sin^{2} θ = \frac{25}{16} \\ or \cos θ = \frac{3}{4} \end{aligned}$

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