The question states:
Find the equation of the following circles: A circle has its centre on the line x + y = 1 and passes through the origin and the point (4,2).
What I did to try to solve this is draw it out and then I tried these two methods which were wrong
- Found a line with (0,0) and (4,2) and intersected it with x + y = 1. Then from there find the equation
- Tried and assumed that the line from (0,0) and (4,2) was the diameter and find the midpoint. Then from there find the equation.
So I was wondering a) why what I did was incorrect b) hints on how to solve it.
In general, I often struggle with a lot of circle coordinate geometry questions and was wondering if you had any tips on how to become better, or see it in a way where I would be able to answer it properly.