Moving a Circle in a Parabola

ice cream

steepness k

1

y coordinate c of center

4.25

answer

This Demonstration shows that the center

B

of a unit circle tangent to the parabola

y=

2

x

is at (0, 5/4). In addition, the segment connecting the point

B

and the tangent point

A

makes a 60° angle with the vertical axes of the parabola.

The radius of the tangent circle with center on the

y

axis at

(0,c)

is

r=

(4ck-1)

(2k)

, where

k

is the steepness of the parabola

y=k

2

x

.