MathDB

A parabola

p

is drawn on the coordinate plane — the graph of the equation

y =-x^2

, and a point

A

is marked that does not lie on the parabola

p

. All possible parabolas

q

of the form

y = x^2+ax+b

are drawn through point

A

, intersecting

p

at two points

X

and

Y

. Prove that all possible

XY

lines pass through a fixed point in the plane. P.A.Kozhevnikov

Problem Statement