Question

Write the standard form of the equation of the circle that passes through the points at (4,5), (-2,3), (-4,-3).

I have gotten to the point of the system of equations but do not know know how to proceed.

I have: 4D + 5E + F + 41 =0
-2D + 3E + F + 13 =0
-4D - 3E + F + 25 =0

Any help would be great!

Answer 1

I'm afraid I don't recognise the equations in C, D and E you've written down - but I've just sketched out the problem on a piece of graph paper. If it helps you to check your working, the centre of the circle ought to be at (3, -2) and the radius is sqrt(50). That would make the equation (X-3)² + (Y+2)² = 50², which you can check easily by just feeding in your three sets of coordinates, since all three lie on the circumference of the circle. But just writing that down without the working won't be enough: you'll need to use your own methods to get there. Good luck!