2023 WSMO Team Round Problems/Problem 12

Problem

Consider parabola $\mathcal P$ pointing upwards with vertex at the origin of the Cartesian plane. Denote the focus of it as $F$ and the directrix of it as $\mathcal L$ . Point $P$ with $x$ -coordinate $4$ is selected in $\mathcal P$ . The perpendicular bisector of $FP$ meets $\mathcal L$ at $Q$ . Given the $x$ -coordinate of $Q$ is $3$ , then $FP^2 = \frac{m}{n},$ for relatively prime positive integers $m$ and $n.$ Find $m+n.$

Page

Toolbox

Search

2023 WSMO Team Round Problems/Problem 12

Problem

Solution