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 all the points on the curve $x^2+y^2-10 x=0$ are reflected about the line $y=x+3$. If the locus of the reflected points is in the form $x^2+y^2+g x+f y+c=0$, then the value of $(g+f+c)$ is