MathDB

Let

A, B

be two variable points on a parabola

P_{0}

, such that the tangents at

A

and

B

are perpendicular to each other. Show that the locus of the centroid of the triangle formed by

A,B

and the vertex of

P_0

is a parabola

P_1 .

Apply the same process to

P_1

and repeat the process, obtaining the sequence of parabolas

P_1, P_2 , \ldots, P_n

. If the equation of

P_0

y=m x^2

, find the equation of

P_n .

B2