1. In the Cartesian coordinate plane, given three points $M(0,0), P(0,5), Q\left(\frac{12}{5}, \frac{9}{5}\right)$, let $A=\{$ circles passing through point $M$ $\}$, $B=\{$ circles passing through point $P$ $\}, C=\{$ circles passing through point $Q$ $\}$, then the equation of the curve on which the point set $A \cap B \cap C$ lies is $\qquad$ .
1. $x^{2}+\left(y-\frac{5}{2}\right)^{2}=\frac{25}{4}$