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 is the required equation of the circle.