What is the Parametric Equation of a circle?
Every equation of a circle depends on particular parameters of that circle and also changes according to them. For example, the parametric equation of a circle is a specific type of equation that keeps changing according to the angle of the points with respect to the origin.
In simple words, if you write two parametric equations of a circle with reference points in the first and third quadrants, both equations will be different as the angle will be changed between the reference points and the origin. Multiple parametric equations can be written for one circle by changing the measurement of the angle or position of the points with respect to the origin.
Don’t you know how you can find this type of equation of a circle? You should read about the process in detail here on this page.
How to find the Parametric Equation of a circle?
To find the parametric equation, you need to know the radius of the circle and the angle made by the reference point on the origin. Once you have these parameters, you can easily find the parametric equation of a circle using the following formula.
x = rcos𝜽 + g
y = rsin𝜽 + h
In the above equation,

“g” represents the x coordinate of the reference point.

“h” represents the y coordinate of the reference point.

“𝜽” is the angle subtended by the reference point on the origin.
Fun Fact: If the reference point is at the origin, then the terms “g” and “h” will be removed from the above equations.
We can write the above equation in different forms using the above formulas and equations. Undoubtedly, you might be unable to understand the formulas and solve the problems for finding the parametric equation of a circle.
To overcome this problem, you can use the Equation of a Circle Calculator that has been designed for this calculation. Using this online tool, you can find the parametric equation of any circle within seconds. Its interface is pretty simple which enables you to insert the values and get the answer without manual interference
How to calculate the Parametric Equation of a circle?
To demonstrate the process of finding the parametric equation of a circle, we have solved an example here. Just have a look at this example and you will understand the procedure better.
example1:
Write the parametric equation of a circle if its radius is 4m.
Solution:
The statement shows that the center is at the origin because we only have the value of the radius. So, the above equations become:
x = rcos𝜽
y = rsin𝜽
By putting the values of radius in these equations, we get:
x = 4cos𝜽
y = 4sin𝜽
These are the parametric equations of the circle with radius 4m.
Conclusion
The above blog has been written in a proper pattern to make it easy to understand for every student. We hope you have learned from this guide and are ready to solve the problems related to this type of equation of a circle.
If you are looking for assistance in your work, you can use the Equation of a circle calculator. It will help you in finding different types of equations of a circle.
FAQ
What is the parametric equation for a circle?
The parametric equation of a circle represents the variation in the equation of a circle with respect to the angle subtended by the reference point on the origin.
What is the parametric equation of a circle not centered at the origin?
If the circle is not centered at the origin, the parametric equation of a circle will be:
x = rcos𝜽 + g
y = rsin𝜽 + h
What is the parametric equation formula?
To find the parametric equation of a circle, you can follow these equations:
x = rcos𝜽 + g
y = rsin𝜽 + h
If your circle is centered at the origin, then you only need to remove “g” and “h” from the equations.
What does a parametric equation show you?
The parametric equation describes the position of the point on the circumference of the circle for which the equation has been written.
Why are parametric equations important?
The parametric equations are important in different practical fields of life. For example, these are used in Engineering, road trafficking for speed checking, and location analysis in the field of aviation.