A system of circles is said to be coaxial when every pair of the circles has the same…

A system of circles is said to be coaxial when every pair of the circles has the same radical axis. It follows from this definition that :
1 . The centres of all circles of a coaxial system lie on one straight line, which is perpendicular to the common radical axis.
2 . Circles passing through two fixed points form a coaxial system for which the line joining the fixed points is the common radical axis.
3 . The equation to a coaxial system, of which two members are S₁ = 0 and S₂ = 0, is S₁ + λS₂ = 0, λ is parameter. If we choose the line of centres as x–axis and the common radical axis as y–axis, then the simplest form of equation of coaxial circles is x² + y² + 2gx + c = 0 ...(1)
where c is fixed and g is arbitrary.
If g = ± \(\sqrt{\mathrm{c}},\) then the radius \(\sqrt{\mathrm{g}^{2}-\mathrm{c}}\) vanishes and the circles become point circles. The points (± \(\sqrt{\mathrm{c}},\)0) are called the limiting points of the system of coaxial circles given by (1).
The equation of the circle which belongs to the coaxial system of circles for which the limiting points are
(1, –1), (2, 0) and which passes through the origin is