MathDB

A variable tangent

t

to the circle

C_1

, of radius

r_1

, intersects the circle

C_2

, of radius

r_2

A

and

B

. The tangents to

C_2

through

A

and

B

intersect in

P

. Find, as a function of

r_1

and

r_2

, the distance between the centers of

C_1

and

C_2

such that the locus of

P

when

t

varies is contained in an equilateral hyperbola.
Note: A hyperbola is said to be equilateral if its asymptotes are perpendicular.

Problem Statement