# Equations of Circles Spring 2014 with Answer Key (Editable)

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I start out class with a 15-minute "mini-lesson," giving my students some basic examples of what today's lesson will be about. I start out with a graph of two points on my overhead projector, such as (6, 7) which is the center of the circle, and (9, 11), which is a point on the circle, and then we figure out the radius of the circle by application of the Pythagorean Theorem to get a radius of 5.

Then, I show them the equation of a circle on the projector. I have found it incredibly helpful to project a graph on my screen using desmos.com, which has the link below:

https://www.desmos.com/

Click on the large, red "launch calculator" button;

Type in the equation of any graph you want. You don't have to "solve for y" first, as you would on a graphing calculator. For example, if you type in (x-3)^2+(y+8)^2=4^2, it will graph the circle for you.

If you type in an equation with constants such as (x-h)^2+(y-k)^2 = r^2, it will ask you if you want to create "sliders" for h, k, r, or "all." If you select "all," it will create three sliders, which you can use to manipulate the equation of the circle.

Note: I actually type in the equation (x+h)^2+(y+k)^2 = r^2, so that students see that adding a constant to x actually moves the graph to the left, and adding a constant to y (within the parentheses) moves the center of the circle down.

It doesn't take long for students to see how the three constants h, k, and r affect the graph of the circle. Using the online calculator, I have found, is much more useful than trying to type in equations into a TI calculator.

Once the mini-lesson is over, I have them get to work within their groups on this worksheet.

The file includes spiral review problems.

This worksheet is intended to be written on directly.

Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.

Immediately before this worksheet, I use the worksheet named 'Transformations of Quadratic Functions for Geometry Spring 2014' (http://www.teacherspayteachers.com/Product/Transformations-of-Quadratic-Functions-for-Geometry-Spring-2014-1269868), and immediately after this worksheet, I use the assessment named 'Geometry Group Practice Test Circles Spring 2014' (http://www.teacherspayteachers.com/Product/Geometry-Group-Practice-Test-Circles-Spring-2014-1269882)

Keywords: Jonnard
Total Pages
3 + Key
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Teaching Duration
1 hour
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\$4.99