Parametric equations and polar coordinates
Plot a curve from parametric equations point by point, eliminate the parameter, model a motion and convert polar coordinates to Cartesian.
- UK: Year 13
- Syria: grade 11
Guide
Sometimes x and y both depend on a helper variable t (the parameter): x = 2t, y = t2. Each t gives one point and many values of t draw the curve. To eliminate the parameter, make t the subject of one equation and substitute it into the other: t = x2 and y = (x2)2.
The parameter is often time. The path of a ball can be modelled with x = vt and y = ut − 12gt2; the ball lands when y = 0.
In polar coordinates a point is given by its distance r from the origin and its angle θ from the positive x-axis. Converting: x = rcosθ, y = rsinθ. A polar curve such as r = 2 + 2cosθ is plotted point by point from a table of (θ, r).