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Question
The parametric equations of a parabola are x = t2 + 1, y = 2t + 1. The cartesian equation of its directrix is
Options
x = 0
x + 1 = 0
y = 0
none of these
Solution
x = 0
Given:
x = t2 + 1 (1)
y = 2t + 1 (2)
From (1) and (2):
\[x = \left( \frac{y - 1}{2} \right)^2 + 1\]
On simplifying: \[\left( y - 1 \right)^2 = 4\left( x - 1 \right)\]
Let \[Y = y - 1 \text{ and } X = x - 1\]
∴ \[Y^2 = 4X\]
Comparing it with y2 = 4ax:
a = 1
Therefore, the equation of the directrix is X = −a , i.e.
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