### Writing equations of circles

The general equation of a circle whose center is located at the point $$\left( {h,k} \right)$$ and whose radius is $$r$$ is given by

$${\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2}$$

Now we can just plug-n-chug this formula to write the equations of any circle we want.

Example:Write the equation of a circle whose center is $$\left( {6, - 6} \right)$$ and with circumference $$2\pi \sqrt {62}$$.

Solution:  We have the coordinates of the center of the circle.  Now we simply need to break down the circumference and figure out what the radius is.  We know that

$$Circumference = 2\pi r$$

so that

$$2\pi r = 2\pi \sqrt {62}$$

$$r = \sqrt {62}$$

So the radius is $$\sqrt {62}$$. We plug-n-chug:

$${\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2}$$

$${\left( {x - 6} \right)^2} + {\left( {y - \left( { - 6} \right)} \right)^2} = {\left( {\sqrt {62} } \right)^2}$$

$${\left( {x - 6} \right)^2} + {\left( {y + 6} \right)^2} = 62$$

Then the general equation of the circle with the information given is

$${\left( {x - 6} \right)^2} + {\left( {y + 6} \right)^2} = 62$$

EXAMPLE:  Write the equation of the circle with center $$\left( {4,6} \right)$$ and circumference $$8\pi$$.

SOLUTION:  We have

$$circumference = 2\pi r$$

so that

$$2\pi r = 8\pi$$

$$r = 4$$

Then the equation is

$${\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2}$$

$${\left( {x - 4} \right)^2} + {\left( {y - 6} \right)^2} = 16$$

3161 x

Use the information provided to write the equation of each circle.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

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2476 x

Use the information provided to write the equation of each circle.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Watch bellow how to solve this example:

2620 x

Use the information provided to write the equation of each circle.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Watch bellow how to solve this example:

### Geometry

Circles
Congruent Triangles
Constructions
Parallel Lines and the Coordinate Plane
Properties of Triangles

### Algebra and Pre-Algebra

Beginning Algebra
Beginning Trigonometry
Equations
Exponents
Factoring
Linear Equations and Inequalities
Percents
Polynomials