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

Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x² + y² $$-$$ 4x $$-$$ 6y + 9 = 0 changes to

The angle between a pair of tangents drawn from a point P to the circle x² + y² + 4x $$-$$ 6y + 9sin²$$\alpha$$ + 13cos²$$\alpha$$ = 0 is 2$$\alpha$$. The equation of the locus of the point P is