First slide

Ellipse

Question

$The distance of a point on the ellipse \frac{x^{2}}{6} + \frac{y^{2}}{2} = 1 from the$ $centre is 2 . Then the eccentric angle of the point is$

Moderate

A

$\frac{π}{4}$
B

$\frac{3 π}{4}$
C

$\frac{5 π}{6}$
D

$\frac{π}{6}$

Solution

$Any point on this ellipse is (\sqrt{6} \cos ϕ, \sqrt{2} \sin ϕ)$
$\begin{array}{l} Here centre is (0, 0), so 6 \cos^{2} ϕ + 2 \sin^{2} ϕ = 4 \\ \Rightarrow 2 \cos^{2} ϕ = 1 \\ \Rightarrow \cos^{2} ϕ = {(\frac{1}{\sqrt{2}})}^{2} = \cos^{2} \frac{π}{4} \\ \Rightarrow ϕ = \frac{π}{4} or \frac{3 π}{4} \end{array}$

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