Given 2 points and a line which contains the center point

Question

Find the general equation of the circle containing $(-4,-2)$ and $(2,0)$, and whose center is contained on the line $5x-2y=19$.

Answer 1

Hint:

The center of the circle is the common point of the perpendicular bisector line of the segment that has as extremes the two given points, $A=(-4,-2)$ and $B=(2,0)$, and the given straight line : $5x-2y=19$.