Let and consider the parabola

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

Problem

Let

a>0

and consider the parabola

x^{2}=4ay

. A point

P(k,2ak)

, where

k

is a real number, is taken in the plane. (i) Substitute the coordinates of

P

in the equation of the parabola and obtain the condition that must be satisfied by

k

for

P

to lie on the curve. (ii) Solve the condition obtained in part (i) to find all possible values of

k

in terms of

a

. (iii) Hence write down the coordinates of every point of the form

(k,2ak)

that belongs to the parabola.