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