2024 SSMO Speed Round Problems/Problem 7

Problem

Let $S$ denote the set of all ellipses centered at the origin and with axes $AB$ and $CD$ where $A=(-x,0),B=(x,0),C=(0,-y),$ and $D=(0,y),$ for $2 \mid x+y$ and $0\le x,y \le 10.$ Let $T$ denote the set of similar ellipses centered at the origin and passing through $(x,y)$ for $2 \nmid x+y$ and $0\le x,y,\le 10.$ If the positive difference between the sum of the areas of all ellipses in $T$ and the sum of the areas of all the ellipses in $S$ is $m\pi,$ find $m.$

Page

Toolbox

Search

2024 SSMO Speed Round Problems/Problem 7

Problem

Solution