Hello, prasum!

is the distance from to (-1,0).

is the distance from to (1,0).

Code:| P | o | * * * | * A * | * B - - o - - - - + - - - - o - - -1 | 1 |

We want points so that: .

[This is known as the Circle of Apollonius.]

We have: .

Square: .

which simplifies to: .

. . . . . . . . . . . . . . . .

Complete the square: .

. . . . . . . . . . . . . . . . . . . . .

Therefore, the circle has center radius