MathDB

2

Part of 2000 AIME Problems

Problems(2)

Point Reflections

Source:

1/5/2007
Let uu and vv be integers satisfying 0<v<u.0<v<u. Let A=(u,v),A=(u,v), let BB be the reflection of AA across the line y=x,y=x, let CC be the reflection of BB across the y-axis, let DD be the reflection of CC across the x-axis, and let EE be the reflection of DD across the y-axis. The area of pentagon ABCDEABCDE is 451. Find u+v.u+v.
geometrygeometric transformationreflectionrectanglesearch
Hyperbola Lattice Points

Source:

12/8/2005
A point whose coordinates are both integers is called a lattice point. How many lattice points lie on the hyperbola x2āˆ’y2=20002.x^2-y^2=2000^2.
conicshyperbolaanalytic geometryalgebradifference of squaresspecial factorizations