A) \[\frac{1}{\sqrt{2}}\]
B) \[\frac{1}{\sqrt{3}}\]
C) \[\sqrt{2}\]
D) \[\sqrt{3}\]
Correct Answer: A
Solution :
Let \[S(ae,0)\]and \[S(-ae,0)\]are foci of an ellipse and \[B(0,b)\]is the positive end of minor axis. \[\therefore \] Slope of \[SB=\frac{b-0}{0-ae}=-\frac{b}{ae}\] and slope of SB\[=\frac{b}{ae}.\] Since SB and SB are perpendicular to each other \[\therefore \] \[\left( -\frac{b}{ae} \right)\left( \frac{b}{ae} \right)=-1\] \[\Rightarrow \] \[{{b}^{2}}={{a}^{2}}{{e}^{2}}\] But \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\] \[\therefore \] \[{{a}^{2}}-{{a}^{2}}{{e}^{2}}={{a}^{2}}{{e}^{2}}\] \[\Rightarrow \] \[{{a}^{2}}=2{{a}^{2}}{{e}^{2}}\] \[\Rightarrow \] \[e=\frac{1}{\sqrt{2}}\]You need to login to perform this action.
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