A) ab
B) \[ab{{e}^{2}}\]
C) \[abc\]
D) ab/e
Correct Answer: C
Solution :
Given equation of an ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] ??(i) The area of \[\Delta \,SPS'=\frac{1}{2}\left[ \begin{matrix} ae & 0 & 1 \\ a\cos \theta & b\sin \theta & 1 \\ -ae & 0 & 1 \\ \end{matrix} \right]\] Expanding w.r. to \[{{C}_{2}}\] \[=\frac{1}{2}(b\,\sin \theta )\,(ae+ae)\] \[=abe\,\sin \theta \] \[[\because \,-1\le \sin \theta \le 1]\] Here, \[S'\to (-ae,0)\] \[S\to (ae,0)\] Now, maximum value of area = abe (maximum value of \[\sin \theta \]) \[=abe\,(1)=abe\]You need to login to perform this action.
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