The curve is given by

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

The curve

C

is given by

y^{2}=4ax

, where

a\neq 0

. (i) Using the geometric definition of a parabola, explain why the focus of

C

lies on the

x

-axis. (ii) Prove that the directrix of

C

is the line

x=-a

. (iii) Without further algebraic calculation, determine whether the parabola opens to the right or to the left for: (a)

a>0

, (b)

a<0

. (iv) On the same set of axes, sketch the parabolas corresponding to

a=3

and

a=-2

, clearly indicating their vertices, axes and directrices.