# Calculating the Apollonius Circle

This is a followup to a question I asked earlier.

I have looked for an example on Google and StackExchange, but I have yet to see a clear example of the formula to determine the equation of an Apollonian Circle given two points and a ratio.

For example, if I have points $A = (0, 0)$ and $B = (3, 1)$ and want to maintain a ratio of $11:13$ between them, how could I get the Apollonian Circle?

I am far from being good at interpreting condensed mathematical notation (which is why this answer did not help me), so a step-wise process would be appreciated.

• What have you done? What have you tried? Which step are you stuck at? – Calvin Lin Dec 7 '13 at 16:31

Giving a point $(x,y)$, we want to find those that satisfy
$$13 \sqrt{x^2+y^2} = 11 \sqrt{(x-3)^2 + (y-1)^2}.$$
$$(x-h)^2 + (y-k)^2 = r^2.$$