What Is the Basic Equation of a Circle? (Mathematics Lesson)
What Is the Basic Equation of a Circle?The equation of a circle centered at the origin is:
where r is the radius of the circle.
Real Examples of Equations of Circles
- A circle with a radius of 4 will have the equation:
- A circle with a radius of 2 will have the equation:
- A circle with a radius of 9 will have the equation:
Why the Equation of a Circle WorksThe slider below explains the equation of a circle:
The Equation of a Circle that Is Not Centered at the OriginThe equation of a circle discussed above is for circles centered at the origin.
If a circle is not centered at the origin, but at a point (a, b), the equation of a circle is:
Read more about the equation of a circle that is not centered at the origin
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.
WHAT DOES AN EQUATION OF A CIRCLE MEAN?
A circle is a set of points.
Each point can be described using Cartesian coordinates: (x, y).
For each point there is a relationship between x and y, given by the equation:
This is true for all points on the circle.
For example, a circle has a radius of 2. Its equation is:
x2 + y2 = 4
Consider the point at (2, 0).
At this point x = 2 and y = 0. Inserting these values into the equation:
22 + 02 = 4
The equation is satisfied.
Consider another point (√2, √2):
At this point x = √2 and y = √2. Inserting these values into the equation:
√22 + √22 = 2 + 2 = 4
Again, the equation is satisfied.