MathDB

The curve y=x^3

Source:

September 13, 2010

analytic geometrygeometry proposedgeometry

Problem Statement

Let

C

be the curve determined by the equation

y = x^3

in the rectangular coordinate system. Let

t

be the tangent to

C

at a point

P

of

C

; t intersects

C

at another point

Q

. Find the equation of the set

L

of the midpoints

M

of

PQ

as

P

describes

C

. Is the correspondence associating

P

and

M

a bijection of

C

on

L

? Find a similarity that transforms

C

into

L.

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