A) \[9a-9{{a}^{2}}-2{{c}^{2}}<0\]
B) \[6ac+9{{a}^{2}}-2{{c}^{2}}<0\]
C) \[9ac-9{{a}^{2}}-2{{c}^{2}}>0\]
D) \[6ac+9{{a}^{2}}-2{{c}^{2}}>0\]
Correct Answer: C
Solution :
Radius of the circle having SS' as diameter is \[r=ae\] if it cuts an ellipse then r > b \[ae>b\Rightarrow \,{{e}^{2}}=\frac{{{b}^{2}}}{{{a}^{2}}}\] \[{{e}^{2}}>1-{{e}^{2}}\] \[{{e}^{2}}>\frac{1}{2}\] \[e>\frac{1}{\sqrt{2}}\Rightarrow \,e\in \,\,\left( \frac{1}{\sqrt{2}},\,1 \right)\]You need to login to perform this action.
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