What is the standard equation of a circle?
Before understanding the standard equation of a circle, you must learn what a circle is. A circle is a specific geometrical figure that is considered a set of points joined together having a fixed distance from a particular point called the center of a circle.
The standard equation of a circle is a particular equation that explains this definition and shows whether a given point is on the circumference of a circle or not. In simple words, this equation explains whether the point is part of a circle or it is beyond or behind the boundary of this figure.
You can find this type of equation of a circle using a specific formula that we will share later on this page. Keep reading to understand what this equation is and how to find it.
How to find the standard equation of a circle?
Finding the standard form equation of a circle is pretty simple because of its easy-to-understand formula. Here is the formula using which you can find this type of equation of any circle.
(x - h)2 + (y - k)2 = r2
In this equation, “x” and “y” are variables on the basis of which this equation will be written while “h” and “k” are the coordinates of the point that we have to check or for which we have to write the equation. “r” is the radius of the circle that is the distance of the point on the circumference of the circle from its center.
Solving squares given in the equation or adding the resultant may be a little difficult. You can get help from the Equation of a Circle calculator to get the equation of any circle quickly. This calculator will find three types of circle equations simultaneously using the data you have put in it.
Using this calculator, you can find the parametric equation of a circle and the general form equation of a circle.
How to calculate the standard equation of a circle?
To make the process of standard equation of a circle calculation easier, we have solved an example here. We hope you will get a better idea about the solution by checking this example.
example1:
Find the standard equation of a circle having a center at (-2, 5) while the radius is 5m.
Solution:
From the above statement, we know that
h = -2
k = 5
and
r = 5
So, the above equation will become:
(x -(-2) )2 + (y - 5)2 = (5)2
x2 + 4x + 4 +y2 - 10y + 25 = 25
By solving this equation, we get:
x2 +y2 + 4x - 10y + 4 = 0
This is the standard equation of a circle having center at (-2, 5) and the measurement of radius 5m.
Conclusion
It might be possible that you have cleared all your doubts about the standard equation of a circle after reading this blog. We have shared the solved examples too for a better understanding of the process of equation calculation.
To get assistance, you can use the Equation of a Circle calculator that can find all three major types of equations of a circle within seconds. By using this maths calculator, you can also understand the process and try to find such equations manually.
FAQ
How do you write an equation of a circle in standard form?
The standard equation of a circle can be written in the following format:
(x - h)2 + (y - k)2 = r2
What is the standard form of a circle example?
The standard form of a circle is the condition when its center lies at the origins (0, 0).
How do you solve standard form examples?
To solve the standard equation of a circle, we only have to insert the values for “h” and “k”. After the insertion of values, we can solve the equation and find the final results.
What is needed to determine the standard equation of a circle?
To determine the standard equation of a circle, we need the point representing the center and the measurement of the radius of the circle.
What does the standard equation of a circle do?
Using the standard equation of a circle, we can find whether the point lies on the circumference of the circle or not.
How do you reduce an equation to standard form?
To reduce the equation to the standard equation of a circle, we need to complete the square for both “x” and “y”.
