Parametric equations
x = f(t), y = g(t). The parameter t generates the curve.
Y13 Pure. Curves not easily described as y = f(x) (e.g. circles, ellipses) parametrise nicely. Eliminate t to get a Cartesian equation, or differentiate dy/dx = (dy/dt)/(dx/dt).
Worked examples
Circle radius r: x = r cos t, y = r sin t.
Ellipse: x = a cos t, y = b sin t.
If x = t², y = t³, then dy/dx = (3t²)/(2t) = 3t/2.
Frequently asked questions
Why bother?
Some curves are awkward in Cartesian form. Parametric is clean and natural for circles, projectiles.
Domain of t?
Specified by the question. For a full circle: 0 ≤ t < 2π.