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# Parametric Equation of a Circle

In coordinate Geometry, the locus of all points in a Circle which satisfy the equations
⇒ x = r cos (p) and y = r sin (p); where x, and y are the coordinates of any Point on the circle, r denotes the radius of the circle and ‘p’ denotes the parameter of a circle. Now, we will see the parametric equation of a circle.
To solve the parametric equation of a circle we have to find the coordinates of any point on the circle. It is also necessary to find the radius of a circle. Basically, we can say that, a circle centered at origin which has radius ‘r’. So, the parametric equation of a circle is given by: x = r cos (p) and y = r sin (p), for every value of p.
So we can say that, any point that is not present on the circle will not satisfy the pair of equation. Suppose we have a radius of a circle as 25 with its center at origin then the circle can be described by the pair of equation. So, we can write the parametric equation of a circle as:
⇒ x = 25 cos (p) and y = 25 sin (p); in this equation value of angle ‘p’ is known as parameter and value of parameter is not plotted on the axis of circle.
Now we will see, what happen if the Center of Circle is not at origin Position? In this case, we have to add and subtract fixed value to x and y coordinates. Let ‘a’ and ‘b’ are coordinates of the center of a circle then we have to add ‘a’ and ‘b’ to x and y coordinates. So the parametric equation as:
⇒ ⇒ x = a + r cos (p) and y = b + r sin (p);
This is all about parametric equation of a circle.