A) 4 units
B) 3 units
C) \[\sqrt{12}\] units
D) \[\frac{7}{2}\] units
Correct Answer: A
Solution :
Eccentricity \[(e)=\sqrt{1-\frac{{{a}^{2}}}{{{b}^{2}}}}\] and foci are \[S(+ae.0)\] and \[{{S}_{1}}(-ae,0)\]. The equation of an ellipse is \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\] Here, \[a=4,\,b=3\] \[\therefore \] \[e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}\] \[=\sqrt{1-\frac{9}{16}}=\frac{\sqrt{7}}{4}\] \[\therefore \] Foci of an ellipse are \[(\pm \sqrt{7},0)\]. \[\therefore \] Radius of required circle \[=\sqrt{{{(\sqrt{7}-0)}^{2}}+{{(0-3)}^{2}}}\] \[=\sqrt{7+9}\] \[=\sqrt{16}=4\] units
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