Determine the equation of a circle containing the origin with an x-intercept of -4 and a y-intercept of 6.

Question

For this problem, I initially solved it using the equation of a circle passing through 3 given points; however, I feel that the method I used isn't the best solution.

My current answer is (x + 2)^2 + (y - 3)^2 = 13. Did I manage to accurately determine the equation needed? I'd appreciate some guidance since I've been mulling over this for ages and I've tried lots of methods that just don't seem to work.

Answer 1