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  • For an ellipse<img alt="\mathrm{\frac{x^2}{25}+\frac{y^2}{16}=1, \theta_1 \text { and } \theta_2}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfra

For an ellipse\mathrm{\frac{x^2}{25}+\frac{y^2}{16}=1, \theta_1 \text { and } \theta_2} are the eccentric angles of points P and Q respectively. If \mathrm{\left|\theta_1\right|+\left|\theta_2\right|=\pi} , then 

 

Option: 1

point P and Q are in opposite quadrant


Option: 2

line PQ is parallel to major axis 


Option: 3

line PQ always passes through centre of ellipse


Option: 4

none of these  

 


Answers (1)

best_answer

\mathrm{\text { As eccentric angle } \theta \in[0,2 \pi) \Rightarrow\left|\theta_1\right|+\left|\theta_2\right|=\pi \quad \Rightarrow \quad \theta_2=\pi-\theta_1}

If \mathrm{P\left(5 \cos \theta_1, 4 \sin \theta_1\right), Q\left(5 \cos \theta_2, 4 \sin \theta_2\right) or Q\left(-5 \cos \theta_1, 4 \sin \theta_1\right)\Leftrightarrow \quad P Q \equiv y=4 \sin \theta_1}

Posted by

Sanket Gandhi

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