MathDB

2

Part of 2007 Hungary-Israel Binational

Problems(2)

Nice Inequality with Partial Sums of Squares

Source: Hungary-Israel Mathematical Competition 2007 Problem 2

11/19/2007
Let a,b,c,d a,b,c,d be real numbers, such that a^2\le 1, a^2 \plus{} b^2\le 5, a^2 \plus{} b^2 \plus{} c^2\le 14, a^2 \plus{} b^2 \plus{} c^2 \plus{} d^2\le 30. Prove that a \plus{} b \plus{} c \plus{} d\le 10.
inequalitiesinequalities unsolvedalgebra
A locus with an ellipse

Source: Hungary-Israel Mathematical Competition 2007 Problem 5

11/19/2007
Given is an ellipse e e in the plane. Find the locus of all points P P in space such that the cone of apex P P and directrix e e is a right circular cone.
conicsellipsegeometry3D geometryspheregeometric transformationrotation