Find the equation of a circle that passes through the points (6,3) ans (-4,-3) and whose center lies on the line y=2x-7

Answer 1

Find the midpoint of the 2 given points
that would be (1,0)
- slope of the line joining those 2 points = 6/10 = 3/5
- so the slope of the right-bisector of the segment joining the two points is -5/3
- equation of that bisector is y = -(5/3)x + b
(1,0) lies on it
0 = -5/3 + b
b = 5/3
the centre must lie on y = -(5/3)x + 5/3 and y = 2x = 7

solve the two equations to find the centre, take it from here