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Equation of Circles

In geometry students are first introduced to the equation of a circle. This is the introductory topic in what we later refer to as conic sections.
by

Jairo Gasiba

on 15 November 2014

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Transcript of Equation of Circles

Circles
More Examples
Check the video out!
Going Further
Check the video out!
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

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
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!
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
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