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Problem 13

The equation of a circle \(C_{1}\) is \(x^{2}+y^{2}=4\). The locus of the intersection of orthogonal tangents to the circle is the curve \(C_{2}\) and the locus of the intersection of perpendicular tangents to the curve \(C_{2}\) is the curve \(C_{3}\). Then : (a) \(C_{3}\) is a circle (b) The area enclosed by the curve \(C_{3}\) is \(8 \pi\) (c) \(C_{2}\) and \(C_{3}\) are circles with the same centre (d) none of these

Expert verified

The correct answers are \(C_{3}\) is a circle (option a), \(C_{2}\) and \(C_{3}\) are circles with the same centre (option c). The area contained by \(C_{3}\) is not \(8\pi\), it is \(4\pi\), hence option b is incorrect, and option d is also incorrect.

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