The parametric equations of a parabola are x = t^2 + 1, y = 2t + … - Vidyadip

MCQ

The parametric equations of a parabola are $x = t^2 + 1, y = 2t + 1$. The cartesian equation of its directrix is

✓
x = 0
B
x + 1 = 0
C
y = 0
D
None of these

✓

Answer

Correct option: A.

x = 0

x = 0

Solution:
Given:
$x=t^2+1 \ldots(1)$
$y=2 t+1 \ldots(2)$
From (1) and (2):
$x=\left(\frac{y-1}{2}\right)^2+1$
On simplifying:
$(y-1)^2=4(x-1)$
Let $Y=y-1$ and $X=x-1$
$\therefore \mathrm{Y}^2=4 \mathrm{X}$
Comparing it with $y^2=4 a x$ :
$a=1$
Therefore, the equation of the directrix is $X=-$ a, i.e. $x-1=-1 \Rightarrow x=0$

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