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equal projections from y=x^2 on x-axis, triangle area (2017 VWO Flanders MO p1)

Source:

August 7, 2020

analytic geometryconicsparabolaequal segmentsarea of triangle

Problem Statement

On the parabola

y = x^2

lie three different points

P, Q

and

R

. Their projections

P', Q'

and

R'

on the

x

-axis are equidistant and equal to

s

, i.e.

| P'Q'| = | Q'R'| = s

. Determine the area of

\vartriangle PQR

in terms of

s