The locus of the centre of the circles which touch both the circles x² + y² = a² and x² + y² = 4ax externally is

The equation of circle of radius $$\sqrt {17} $$ unit, with centre on the positive side of X-axis and through the point (0, 1) is

A variable circle passes through the fixed point A(p, q) and touches X-axis. The locus of the other end of the diameter through A is

If P(0, 0), Q(1, 0) and R$$\left( {{1 \over 2},{{\sqrt 3 } \over 2}} \right)$$ are three given points, then the centre of the circle for which the lines PQ, QR and RP are the tangents is