5.5.1 Parametric equations

Suppose f t ( ) and g t ( ) are functions of ' ' t . Then the equations x f t ( ) and y g t ( ) together describe a curve in the plane . In general ' ' t is simply an arbitrary variable, called in this case a parameter , and this method of specifying a curve is known as parametric equations . One important interpretation of ' ' t is time .

In this interpretation,the equations x f t ( ) and y g t ( ) give the position of an object at time ' ' t . So a parametric equation simply has a third variable, expressing x and y in terms of that third variable as a parameter . A parameter does not always have to be ' ' t . Using ' ' t is more standard but one can use any other variable.

(i) Parametric form of the circle x Let P x y ( , ) be any point on the circle x Join OP and let it make an angle θ with x -axis. Draw PM perpendicular to x -axis. From triangle OPM ,