Parabola as a Locus of Centers of Circles

radius r of center circle

1

vertical line

distance totangent line

3.035

tangent circle centers

1.5

show answer

What is the equation of the parabola?

equation of the given line: x = 3.035

A parabola is the set of all the points that are equidistant from a fixed point

P

(the focus, red point) and a fixed line

d

(the directrix, dashed green line).

Given a circle

C

and a line

l

(in any position relative to

C

), the locus of the centers of all the circles that are tangent to both

C

and

l

is a parabola (dashed red curve) whose focal point

P

is the center of

C

.