MathDB

parabola y=ax^2, OA _|_ OB

Source: Bulgaria 1990 P2

June 9, 2021

conicsparabola

Problem Statement

Let be given a real number

\alpha\ne0

. Show that there is a unique point

P

in the coordinate plane, such that for every line through

P

which intersects the parabola

y=\alpha x^2

in two distinct points

A

and

B

, segments

OA

and

OB

are perpendicular (where

O

is the origin).