Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2024 SSMO Speed Round Problems/Problem 7

Revision as of 15:41, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>S</math> denote the set of all ellipses centered at the origin and with axes <math>AB</math> and <math>CD</math> where <math>A=(-x,0),B=(x,0),C=(0,-y),<...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 $m.$

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2024_SSMO_Speed_Round_Problems/Problem_7&oldid=247917"