Second derivative under parametric form for JEE

Formula

\[\frac{d^2y}{dx^2}=\frac{\dfrac{d}{dt}\left(\dfrac{dy}{dx}\right)}{dx/dt}\]

Variables: \(x=x(t),\ y=y(t)\).

Conditions: \(dx/dt\neq 0\).

Parametric curvature/concavity and tangent questions.