Find the equation of the circle with passes through the points and and has its centre lying on the line
If the points (0,1) and (3,-2) are the endpoints of the diameter of the circle,
then the centre is (1.5,-0.5), the radius is obtained from Pythagoras' theorem.
The equation of the circle then is
However, if the line from (0,1) to (3,-2) is a chord of the circle,
then there are an infinite number of solutions,
since you can choose any point on the line y=x-2 as the circle centre.
The line is perpendicular to the line joining the two given points,
and passes through the midpoint of the chord.