MathDB

Given two points

P,\ Q

on the parabola

C: y=x^2-x-2

in the

xy

plane. Note that the

x

coodinate of

P

is less than that of

Q

.
(a) If the origin

O

is the midpoint of the lines　egment

PQ

, then find the equation of the line

PQ

.
(b) If the origin

O

divides internally the line segment

PQ

by 2:1, then find the equation of

PQ

.
(c) If the origin

O

divides internally the line segment

PQ

by 2:1, find the area of the figure bounded by the parabola

C

and the line

PQ

Problem Statement