Parametric Equations of a Circle
Draw a circle with centre at and with a radius equal to
which is the fixed distance from the centre of the circle. Now let
be any point of the circle as shown in the diagram. Draw a perpendicular from point
on the X-axis, meeting at the point
. Consider the triangle
which is a right angle triangle where
is the base of the right triangle and
is the perpendicular of the triangle.

From the basic ratios of trigonometry,
Since ,
,
, putting these values in equation (i) and (ii) we get the following equations:
These equations are the called the parametric equations of a circle.
Example: Show that the parametric equations and
represent the equation of circle
.
Solution: We have been given parametric equations,
Now squaring and adding equation (i) and (ii), we get
Hence
