Determining which points cannot lie on a circle

Question

A circle passes through the points $(3,4)$ and $(5,7)$. Which of the following points CANNOT lie of circle?

A) $(-2,-1)$

B) $(3,2)$

C) $(5,5)$

D) $(6,4)$

E) $(-1,-2)$

Any help is appreciated.

Answer 1

Any $3$ non collinear points can form a triangle, and thus all the $3$ points will lie on the circumcircle of the triangle. Thus the required condition so that they do not lie on the circle is that they lie on the same line which is satisfied by $(-1,-2)$