**Circles**

More Examples

Check the video out!

Going Further

Check the video out!

Did you get the answer??

It is C!

1) Center = (0,0) Radius = 4

2) Center = (3,0) Radius = 5

3) Center = (-2,4) Radius = 3

4) Center = (1,-3) Radius = 6

5) Center = (h,k) Radius = r

Figure out the center and radius

for each equation

**Conclusion**

Equations of Circles

Let's Discover the equation of a circle!

Equation of a circle-

(x-h)^2+(y-k)^2= r^2

(h,k) = center of circle

r = radius

Graph

Assignment

The assignment is simple; the student will have a partner and will have to create their own Cartesian plane on a poster board. The teacher will then give each pair 4 equations of circles that can be placed in all of the quadrants. The students have to first graph the equations on a piece of paper and have the teacher approve them before they can complete the final poster board. Once they are approved, the students will then graph the equations on the poster board and use their markers to label the center, and radius of each circle. They will also place the equation for each circle under the circle or next to it.

Going Beyond

On your own

Example

Examples

(x-2)^2 + (y - 3)^2 = 25

Center coordinates are the numbers inside the parentheses with the x and y.

(2,3) Note: make sure you put them with the opposite sign.

The radius is the number at the end BUT you must do the square root of that number because the last number is r^2 = 25. We do the square root and our radius is 5!

Center- (2,3) Radius -5

Notes

In the previous slide, we got to see examples of how the center and radius affect the equation of a circle and how to figure out the center and radius of any given equation.

Remember, (h,k) is the center and r is the radius.

Copy and past the link below for more practice

http://www.regentsprep.org/regents/math/geometry/gcg6/PracCir.htm

Remember, use the equation

(x-h)2 + (y-k)^2 = r^2

This is just the tip of the iceberg!

Circles are part of what we know as

as Conics. Check the video below

for an introduction to conics and see

the picture below for the different types

of conics.

I hope this lesson provided a deeper

understanding of the equation of a circle

and a glimpse into the vast world of conics!

Please remember that you will have a summative assessment next class. Below are the topics that will be covered

Topics

Area and Circumference

Identifying parts of a circle

Arc length and Area of a sector

Constructions with Circles

Proofs with circles

Equation of a circle