In the parabola the latus rectum is the line

MATHEMATICS · Multi-part · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

In the parabola

y^{2}=4ax

the latus rectum is the line

x=a

. A point

R(a,2a)

on this line is reflected in the axis to the point

R'(a,-2a)

. (i) Show that both

R

and

R'

lie on the parabola. (ii) Prove that the chord

RR'

is perpendicular to the axis and that its midpoint coincides with the focus of the parabola. (iii) Find the length of the chord

RR'

and verify that it equals the length of the latus rectum.