Hi all ---

I'm posting this question on geometry here because I'm not sure if you need calculus. But even if you don't, I'd like to know if I can use calculus to do the question.

Question with solution:

Now, I understand perfectly how to complete the square. So when I did this problem, I graphed it and saw that the point on the circle closest to had to be in the 1st quadrant. This is because I can see that the origin is in the upper-right "quarter" of the circle, if I separate the circle into equal 4s.

But I'm not sure how to find the specific point in the 1st quadrant? The solution somehow knows that is the answer, but it doesn't explain how it got it?

Also, I know from calculus that ---

where must be on the circle.

But I can maximize the square instead ---

where must be on the circle.

But this doesn't seem to help, because it looks too complicated to sub in the equation of the circle into ?

Thanks ---