# Moving a Circle in a Parabola

Moving a Circle in a Parabola

This Demonstration shows that the center of a unit circle tangent to the parabola is at (0, 5/4). In addition, the segment connecting the point and the tangent point makes a 60° angle with the vertical axes of the parabola.

B

y=

2

x

B

A

The radius of the tangent circle with center on the axis at is , where is the steepness of the parabola .

y

(0,c)

r=

(4ck-1)

(2k)k

y=k

2

x