The equation of a circle \( C_{1} \) is \( x^{2}+y^{2}=4 \). The lo...

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The equation of a circle \( C_{1} \) is \( x^{2}+y^{2}=4 \). The locus of the intersection of orthogonal tangents to the circles is the curve \( \mathrm{C}_{2} \) and the locus of the intersection of perpendicular tangents to the curve
\( \mathrm{P} \) \( \mathrm{C}_{2} \) is the curve \( \mathrm{C}_{3} \). Then

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(a) \( \mathrm{C}_{3} \) is a circle
(b) the area enclosed by the curve \( \mathrm{C}_{3} \) is \( 8 \pi \)
(c) \( \mathrm{C}_{2} \) and \( \mathrm{C}_{3} \) are circles with the same centre
(d) none of these
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