# 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 is the required equation of the circle.