Parametric equations

What is parametric equations?

Parametric equations express x and y separately as functions of a parameter t, e.g. x = cos(t), y = sin(t). They model curves that aren't conveniently expressed as y = f(x) — including circles, ellipses, and projectile paths. A-Level Maths uses the chain rule dy/dx = (dy/dt) / (dx/dt) to find gradients, and substitution to eliminate the parameter and recover the Cartesian equation.