What Is the Equation of a Circle? (Mathematics Lesson)
What Is the Equation of a Circle?The equation of a circle is:
where (a, b) are the Cartesian coordinates of the center of the circle and r is the radius of the circle.
A Real Example of an Equation of a Circle
This is the equation of the circle centered on (2,3) with a radius of 5 (=√25).
Another Real Example of an Equation of a Circle
This is the equation of the circle centered on (-1,1) with a radius of 3 (=√9).
How to Find the Center and Radius of a Circle from its EquationThe center and radius of a circle can be found by looking at the equation of a circle.
The x-coordinate is -1.
The y-coordinate is 1.
The center of the circle is (-1,1).
The radius is 3.
Read more about how to find the radius of a circle from the equation
Yet Another Example of the Equation of a CircleThe slider below shows another real example of the equation of a circle:
The General Form of an Equation of a CircleThe equation of a circle discussed above is the standard form.
If the squared brackets are expanded, the general form of the equation of a circle is found:
NoteWHAT IS A CIRCLE?
A circle is a shape containing a set of points that are all the same distance from a given point, its center.
PARTS OF A CIRCLEThe center is the point the same distance from the points on the circle.
The radius is the line segment from the center of the circle to any point on the circle.
CIRCLE CENTERED AT THE ORIGINA circle centered at the origin has a centre at (0,0).
If it has a radius r, the equation is:
(x - 0)2 + (y - 0)2 = r2
x2 + y2 = r2
FINDING THE CENTERThe equation of a circle is:
The center is (a,b).
The number in the bracket with the x determines the x-coordinate.
The number in the bracket with the y determines the y-coordinate.
The a and b are being subtracted from the x and y.
This means numbers that are
- negative in the brackets lead to a positive center co-ordinate
- positive in the brackets lead to a negative center co-ordinate.
FINDING THE CENTERDon't be confused if you see an equation which looks like this:
(x - 1)2 + (y - 3)2 - 49 = 0
This is still an equation of a circle:
(x - a)2 + (y - b)2 - r2 = 0