Warm Up

Area & Equation of Circles

May 1st, 2014

What is the area & circumference of a circle?

rC

rA

2

2

Review• Find the area of a circle with r =5

• Find the area of a circle with r = √2

• If the area of a circle is 81𝝅 what is the radius?

Example• Lance decides he would like the

garden to have a circumference of 40π feet. What would be the area of this garden?

ExampleLance is also considering including a

sidewalk around the outside of the garden, as shown below. Determine the area of the sidewalk.

X & Y and H & KA circle is the set of all points in a plane that are equidistant from a given point called the center.

The Equation of a Circle Derived from Pythagorean Theorem

EQUATION OF A CIRCLE

Write the equation of the circle described …• Center (0, 3) and radius = 5

• Center (-1, 5) and radius = 7

Write the equation of the circle….

Write the equation of the circle…

• Center (2, -1) and contains the point (0, 4)

Write the equation of a circle• Endpoints of the diameter (-1,

3) and (5, 1)

Identify the center and radius of the circle…• (x – 3)2 + (y + 1)2 = 49

• x2 + (y – 5)2 = 10

Systems with Circles and Linear Equations

How do we solve algebraically?• We take the linear equation

(solve for y) and plug into the circle

Let’s try one!• Solve by graphing…

Now solve algebraically!• Step 1: Get “y” by itself• Step 2: Substitute linear equation in for “y” in the

circle• Step 3: Multiply out & simplify• Step 4: Factor• Step 5: Plug in x values to get y values

Solve the system by graphing:

Homework

• Worksheet