Algebra

##### Related Lessons

- Adding and Subtracting Scientific Notation
- Adding Fractions
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- Change of Base Formula
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- Commutative Property of Addition
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- Determinant Calculator
- Determinant of a Matrix
- Difference of Squares
- Discriminant
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- Dot Product Calculator
- Eigenvalue Calculator
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- Even Numbers
- Exponent Rules
- Factorial Calculator
- Factoring Calculator
- Fraction Calculator
- Fractional Exponents
- How to Find the Median
- Interval Notation
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- Matrix Multiplication Calculator
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- Midpoint Formula
- Multiplying Negative Numbers
- Negative Exponents
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- One to One Function
- Partial Fraction Decomposition Calculator
- Point Slope Form
- Properties of Multiplication
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- Rationalize the Denominator
- Rectangular to Polar Calculator
- Reflexive Property
- Round to the Nearest Tenth
- RREF Calculator
- Simplify Calculator
- Slope Calculator
- Slope Intercept Form
- Solve for x Calculator
- Standard Form
- Summation Calculator
- Vertex Form

Tutors/teachers:

# Equation of a Circle

#### Lesson Contents

## Common Forms of a Circle's Equation

### Standard Form for the Equation of a Circle

The standard form equation of a circle is given as:

Where *a* is x-coordinate of the circle’s center, *b* is the y-coordinate of the circle’s center, and *r* is the radius of the circle.

Let’s look at a circle defined by the equation (x – 1)^{2} + (y – 2)^{2} = 25. The center of this circle is located at the point (1, 2) since a = 1 and b = 2. The circle’s radius is 5 since r^{2} = 25 and r = 5.

### General Form for the Equation of a Circle

The general form equation of a circle is given as:

Where *A*, *B*, and *C* are constants.

The general form equation is not formatted to give us a quick glimpse of circle location and radius like the standard form equation is. However, general form can be converted to standard form by using the algebraic process known as completing the square.

### Polar Coordinates Equation of a Circle

The standard form and general form of a circle’s equation are expressed in the Cartesian coordinate system. **When dealing with circles, using the polar coordinate system is simpler than the Cartesian coordinate system.**

In polar coordinates, the equation of a circle centered over the origin is:**r = radius of the circle**

If the circle is not centered over the origin but lies on the x-axis, the equation is:**r = 2acosθ**

Where *a* is the x-coordinate of the circle’s center.

If the circle is not centered over the origin but lies on the y-axis, the equation is:**r = 2bsinθ**

Where *b* is the y-coordinate of the circle’s center.

Result :

Worksheet 1

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Cheat sheet

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