A) 1
B) 2
C) 4
D) \[\frac{3}{2}\]
Correct Answer: B
Solution :
Let the points of intersection of the line and the ellipse be\[(a\cos \theta ,\,\,b\sin \theta )\]and \[\left\{ a\cos \left( \frac{\pi }{2}+\theta \right),\,\,b\sin \left( \frac{\pi }{2}+\theta \right) \right\}\], since they lie on the given line\[lx+my+n=0\]. \[la\cos \theta +mb\sin \theta +n=0\] \[\Rightarrow \]\[la\cos \theta +mb\sin \theta =-n\] and \[la\sin \theta +mb\cos \theta +n=0\] \[la\sin \theta -mb\cos \theta =n\] squaring and adding, we get, \[{{a}^{2}}{{l}^{2}}+{{b}^{2}}{{m}^{2}}=2{{n}^{2}}\] \[\Rightarrow \frac{{{a}^{2}}{{l}^{2}}-{{b}^{2}}{{m}^{2}}}{{{n}^{2}}}=2\]
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