Ford circle information

In mathematics, a Ford circle is a circle in the Euclidean plane, in a family of circles that are all tangent to the $x$ -axis at rational points. For each rational number $p/q$ , expressed in lowest terms, there is a Ford circle whose center is at the point $(p/q,1/(2q^{2}))$ and whose radius is $1/(2q^{2})$ . It is tangent to the $x$ -axis at its bottom point, $(p/q,0)$ . The two Ford circles for rational numbers $p/q$ and $r/s$ (both in lowest terms) are tangent circles when $|ps-qr|=1$ and otherwise these two circles are disjoint.^[1]