EllipseHardBloom L3
Question
The eccentric angle of point on the ellipse $x^{2} + 3y^{2} = 6$ at a distance 2 unit from origin is:
Options
A.$\frac{\pi}{4}$
B.$\frac{3\pi}{4}$
C.$\frac{5\pi}{4}$
D.$\frac{7\pi}{4}$
Solution
Sol. $\begin{matrix} & P \equiv (\sqrt{6}cos\theta,\sqrt{2}sin\theta) \\ & 6\cos^{2}\theta + 2\sin^{2}\theta = 4 \\ \Rightarrow & 4\cos^{2}\theta = 2 \\ \Rightarrow & cos\theta = \pm \frac{1}{\sqrt{2}} \end{matrix}$
Hence, $\theta = \frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$
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