Draw a circle with centre at and radius is 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 X-axis meet at the point . Consider the triangle which is a right angled triangle with is the base of the right triangle and is the perpendicular of the triangle.
From the basic ratios of trigonometry,
Since , , , so putting these values in equation (i) and (ii), we get the following equations
These equations are the called the parametric equations of circle.
Example: Show that the parametric equations and represents the equation of circle .
Solution: We have given parametric equations,
Now squaring and adding equation (i) and (ii), we get
Hence is the required equation of circle.