How to calculate the centre of a circle given two points and the equation of a line going through the centre? A(3,5) and b(9,-3) lie on a circle. show that the centre of the circle lies on the line 4y-3x+14 = 0
Is it possible to work out the centre of the circle algebraically since the only method I can think of is drawing the points and the line on a set of axis and estimating the circle's radius.
that was my attempt; ie I worked out the centre by plotting the points and then estimating it. helpfully the centre in this question was a whole number but I want to know how to answer the question properly(give an algebraic solution) 

If $A$ and $B$ lie on a circle, then by definition they’re equidistant from its center. So, write down the standard expressions for the distance of an arbitrary point $(x,y)$ from each of these two fixed points and equate them: $$\sqrt{(x-3)^2+(y-5)^2}=\sqrt{(x-9)^2+(y+3)^2}$$ Now simplify this equation. Start by squaring both sides.
