alleryIf $x = a t^2$, $y = 2 a t$ (parametric), then $\dfrac{dy}{dx}$ equals:
A$2t$
B$1/(2t)$
C$t$
D$1/t$
Answer & Solution
Correct answer: D. $1/t$
$dx/dt = 2at$, $dy/dt = 2a$.
$dy/dx = (dy/dt)/(dx/dt) = 2a/(2at) = 1/t$.
(This parametrises a parabola $y^2 = 4ax$; slope at parameter $t$ is $1/t$.)
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