x=t2+ 1 & y = 2t +1. Tha cartesian equation of its directrix is
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We have the equations
x = t2 +1 …(1)
y = 2t + 1 …(2)
From (1) and (2), we get
(y – 1)2 = 4 (x – 1) …(3)
Let Y = y – 1 and X = x – 1
Then from equation (3) we have
⇒ Y2 = 4X
Equation of the directrix for parabola Y2 = 4X is:
X = –1
⇒ x – 1 = –1
⇒ x = 0
This is the required equation of directrix.