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# Equation of a Circle

## Standard form equation of a Circle

 Equation of Circle Applet Circle Formulas Circle Worksheets
The standard form equation of a circle is a way to express the definition of a circle on the coordinate plane.
• On the coordinate plane, the formula becomes $$(x -h)^2 + (y - k)^2 =r^2$$
• h and k are the x and y coordinates of the center of the circle
• $$(x-9)^2 + (y-6)^2 =100$$ is a circle centered at (9,6) with a radius of 10

# Examples

General Formula

Circle with a center of (4,3) and a radius of 5

Circle with a center of (2, -1) and a radius of 4

#### Definition of Circle

Definition: A circle is the set of all points that are the same distance, r, from a fixed point.
General Formula: X 2 + Y 2=r2 where r is the radius

• Unlike parabolas, circles ALWAYS have X 2 and Y 2 terms.
• X2 + Y2=4 is a circle with a radius of 2 ( since 4 =22)
• Remember that a circle is a locus of points. A circle is all of the points that are a fixed distance, known as the radius, from a given point, known as the center of the circle.
• Explore the standard equation of a circle using the applet below (Go here for a larger version)
 Circle Worksheets Circle Formulas

## Equation of Circle Interactive HTML5 Applet

Explore and discover the standard form equation of a circle using the interactive circle below. To move the circle just click and drag on either of the two points, and the circle's standard form equation will adjust accordingly. You can also see the general form of the circle's equation by clicking 'show general form'
 Radical Form? Show General Form? Equaton Type = < ≤


Practice Problems

What is the equation of the circle pictured on the graph below?

Look at the graph below, can you express the equation of the circle in standard form?

Look at the graph below, can you express the equation of the circle in standard form?
What is the radius of the circles below?
• Y2+X2 =9
• Y2+X2 =16
• Y2+X2 =25
• Y2 + X2 = 11
• Y2 + X2 = a
Look at each standard form equatio below and identify the center and radius.