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JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    If the curves \[{{(x-20)}^{2}}+{{(y-20)}^{2}}={{r}^{2}}\] and \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{1}=100\]intersects orthogonally at a point \[(20\cos \theta ,10\sin \theta )\] then

    A) \[\tan \frac{\theta }{2}=2\]                        

    B) \[\tan \frac{\theta }{2}=\sqrt{2}\]

    C) \[\tan \frac{\theta }{2}=\frac{1}{20}\]                   

    D) \[\tan \frac{\theta }{2}=10\]

    Correct Answer: A

    Solution :

    \[(20,20)\]lies on\[\frac{x(20\cos \theta )}{400}+\frac{y(10\sin \theta )}{100}=1\] \[\cos \theta +2\sin \theta =1\Rightarrow \sin \theta =\frac{1-\cos \theta }{2}\] \[\Rightarrow \tan \frac{\theta }{2}=2\]Ans.


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