Question

The parametric representation of a parabola is x=3+t² , y=2t-1. Its focus is at

Answer 1

It is given that

x = t^2+3 ...(1)

y = 2t - 1 ...(2)

From (1)
t^2= x-3
and (2),
t^2=(y+1)^2/4

we get

(y +1)^2 = 4 (x –3) ...(3)

Let Y = y +1 and X = x – 3

Then

(3) ⇒ Y2 = 4X

Equation of the directrix for parabola Y2 = 4X is:

X = –1

⇒ x – 3 = –1

⇒ x = 3-1=2

This is the required equation of directirx.