The locus of the centre of a circle which passes through two variable points (a, 0), ($$-$$a, 0) is

The intercept on the line y = x by the circle x² + y² $$-$$ 2x = 0 is AB. Equation of the circle with AB as diameter is

If the coordinates of one end of a diameter of the circle $${x^2} + {y^2} + 4x - 8y + 5 = 0$$ is (2, 1), the coordinates of the other end is

Let $x-y=0$ and $x+y=1$ be two perpendicular diameters of a circle of radius $R$. The circle will pass through the origin if $R$ is equal to