- #1

DakMasterFlash

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## Homework Statement

Find the largest circle centered on the positive y-axis which touches the origin and which is above y=x^2

## Homework 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

## 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!