A) \[{{x}^{2}}+{{y}^{2}}=4\]
B) \[{{x}^{2}}+{{y}^{2}}=9\]
C) \[{{x}^{2}}+{{y}^{2}}=5\]
D) \[{{x}^{2}}+{{y}^{2}}=13\]
Correct Answer: D
Solution :
The locus of the point of intersection of the perpendicular tangents to ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is a director circle and whose equation is given by \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] \[\therefore \] Here the equation of director circle \[{{x}^{2}}+{{y}^{2}}=9+4\] \[{{x}^{2}}+{{y}^{2}}=13\]
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