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

Let ABCD be a square of side length 2 units. C_(2) is the fircle through the vertices A, B, C, D and C_(1) is the circle touching all the of the square ABCD. L is a lien through vertex 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 L. The locus of the centre of the circle is

A circle touches the lines x-y- 1 =0 and x -y +1 =0. the centre of the circle lies on the line

Variable circles are drawn touching two fixed circles externally then locus of centre of variable circle is

A circle C touches the x-axis and the circle x ^(2) + (y-1) ^(2) =1 externally, then locus of the centre of the circle C is given by