Finding the center M of a circle through points A(2,3) and B(-1,6)

[DERRAN]

Homework Statement

In the diagram alongside, A(2,3) and B(-1,6) lie on the circle with centre M(c,d).
M is also a point on the straight line defined by 2x + 5y + 1=0. The diagram is on the attached doc file.

Calculate the co-ordinates of M.

Homework Equations

analytical methods only!

The Attempt at a Solution

Im really stuck

 

[quantumdude]

You have 3 unknowns (c, d, and the radius r of the circle), so you need 3 equations to find them. Try to answer the following questions. They should help you.

1.) What is the standard form of the equation form of a circle with center (c,d) and radius r?
2.) What do you get when you plug the point (x,y)=(-1,6) into that equation?
3.) What do you get when you plug the point (x,y)=(2,3) into that same equation?
4.) What do you get when you plug the point (x,y)=(c,d) into the equation of the given line?

That should get you started.

 

[DERRAN]

You have 3 unknowns (c, d, and the radius r of the circle), so you need 3 equations to find them. Try to answer the following questions. They should help you.

1.) What is the standard form of the equation form of a circle with center (c,d) and radius r?
2.) What do you get when you plug the point (x,y)=(-1,6) into that equation?
3.) What do you get when you plug the point (x,y)=(2,3) into that same equation?
4.) What do you get when you plug the point (x,y)=(c,d) into the equation of the given line?

That should get you started.

Thank you I got it. M is (-3,1)