For each parabola *y* = *x*^{2} + *px* + *q* meeting the coordinate axes in three distinct points, a circle through these points is drawn. Show that all of the circles pass through a single point which is (0,1).

Then
*x*^{2}_{1} + *ax*_{1} + *c* = 0
*x*^{2}_{2} + *ax*_{2} + *c* = 0
*q*^{2} + *bq* + *c* = 0
Since *x*_{1}, *x*_{2} are the roots of the equation*x*^{2} + *px* + *q* = 0, it follows that *a* = *p*, *c* = *q* and *b* = − *q* − 1. Then the circle has the equation
*x*^{2} + *y*^{2} + *px* − (*q* + 1)*y* + *q* = 0
and it pass through the point (0,1).