Let the line cut the parabola at points and

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let the line

lx+my=1

cut the parabola

y^2=4ax

at points

A

and

B

. Normals at

A

and

B

meet at point

C

. The normal from

C

, other than these two, meets the parabola at

D

. Then the coordinates of

D

are (1)

(a,2a)

(2)

\left(\frac{4am}{l^2},\frac{4a}{l}\right)

(3)

\left(\frac{2am^2}{l^2},\frac{2a}{l}\right)

(4)

\left(\frac{4am^2}{l^2},\frac{4am}{l}\right)

Related theory

Browse the problem library