1. The problem statement, all variables and given/known data Find the largest circle centered on the positive y-axis which touches the origin and which is above y=x^2 2. Relevant equations equation of a circle: r^2=(x-a)^2+(y-b)^2 equation of a circle centered on the y-axis: x^2+(y-b)^2=r^2 equation of a parabola: y=x^2 3. The attempt at a solution For the life of me, I couldn't figure out how to do this problem. I "eyeballed" the graphs and realized that a circle with a radius of 0.5 perfectly fits the parameters required by the problem statement, but I have no idea how to do this mathematically. A radius of 0.5 yields the equation: x^2+(y-0.5)^2=0.5^2 x^2+y^2-y+0.25=0.25 x^2+y^2-y=0 I've tried (rather aimlessly) taking the derivative of this function, yielding: 2x+2yy'-1y'=0 However, I realize that I should use the generic equation for a circle, which gives me: x^2+(y-b)^2=r^2 x^2+y^2-yb+b^2=r^2 As I'm sure you all can tell, I'm not making much progress as to an actual solution to this problem. I was hoping that you guys could give me some direction and a hint or two. Any help would be appreciated! Thanks!