A) \[\frac{1}{9}\]
B) \[\frac{4}{9}\]
C) \[\frac{1}{3}\]
D) \[\frac{2}{3}\]
Correct Answer: D
Solution :
Let the radius of the circle be a, then the major axis of the inscribed ellipse is of length\[2a\]. |
The required probability |
\[=\frac{\pi {{a}^{2}}-\pi {{a}^{2}}\sqrt{1-{{e}^{2}}}}{\pi {{e}^{2}}}\] |
\[=1-\sqrt{1-{{e}^{2}}}=-\sqrt{1-\frac{8}{9}}=\frac{2}{3}\] |
[Area of ellipse\[=\pi ab=\pi a.a\sqrt{1-{{e}^{2}}},'e'\] being eccentricity.] |
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