First slide

Parabola

Question

Which of the following parametric equation does
not represent a parabola

Moderate

A

$x = t^{2} + 2 t + 1, y = 2 t + 2$
B

$x = a (t^{2} - 2 t + 1), y = 2 a t - 2 a$
C

$x = 3 \sin^{2} t, y = 6 \sin t$
D

$x = a \sin t, y = 2 a \cos t$

Solution

$x = a T^{2}, y = 2 a T$ represents a parabola.
in(a) $a = 1, T = t + 1, in (b) a = a, T = (t - 1)$
in(c) $a = 3, T = \sin t .$ But in $(d) if 2 a T = 2 a \cos t$
$\Rightarrow T = \cos t$ which does not satisfy $x = a T^{2}$

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