Circle EquationsReal World Application

What applications do circle equations apply to?• Earthquakes: the epicenter is the center and the radius is

how far the earthquake can be felt from the center• Towers (cell phone, radio, etc): the tower is the center and

the radius is how far you receive signal from that tower. • Satellite's orbit: the center is the center of the earth and

the radius is the distance the satellite is from the center of the earth.

• Circular path: a tree could be the center and the distance from a tree to the path is the radius.

• These are just a few examples. There are many more!

Want to try one?• The epicenter of an earthquake is (0,0) and it can be felt

up to 25 miles away. Write the equation for this circle.

Answer• The equation for a circle is where (h, k) is the center

and r is the radius. • Plug in your center and radius:

Simplify

Not too bad right? Try this one:• The equation represents the service that a cell phone

tower provides. How far from the tower will you receive cell phone service?

Answer…• Remember the equation of a circle is so the center of

is (0,0). • so r = 34 ( I found this by taking the square root)• The radius represents the distance from the center to

the outside of the circle so with this one, we want the radius.

• Answer: 34 miles