Let A B C D be a square of side length 2 units. C_2 is the circle through vertices A, B, C, D and...

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Let A B C D be a square of side length 2 units. C_2 is the circle through vertices A, B, C, D and C_1 is the circle touching all the sides of the square A B C D . L is a line through A.

A circle touches the line L and the circle C_1 externally such that both the circles are on the same side of the line, then the locus of centre of the circle is:
(a) ellipse
(b) hyperbola
(c) parabola
(d) parts of straight line

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