Date Circles Page #

Circles

Learning Targets for Today:

I can define circle, radius, and center of a circle.

I can write the standard form of a circle using information given.

I can find the intercepts of a circle. I can graph the circle given the

equation by hand and with a graphing calculator.

Circles

CirclesThe figure to the left shows the graph of a circle. To find the equation, we let (x, y) represent the coordinates of any point on a circle with radius r and center (h, k). Then the distance between the points (x, y) and (h, k) must always equal r. That is by the distance formula we have the following:

Distance formula =

In this case r =

Square both sides r2 =

Circles

Write the standard form of the equation of the circle with radius 5 and center (-3, 6).

 

Find the equation of the circle with center (3, -2) and contains the point (-1, 1).

Find the equation of the circle with endpoints on the diameter at (-4, -1) and (4, 1).

CirclesFor the circle (x + 5)2 + (y – 2)2 = 16, find the intercepts, if any, of its graph.

Graphing CirclesGraph the equation (x + 3)2 + ( y – 2)2 = 16

From the equation, we know the center is located at ( , ) and the radius is ____ units.Plot the center point and located the four points vertically and horizontally that are ______ units away from the center. These points can now be used to obtain the graph of the circle.

Graphing CirclesTo graph a circle on a graphing utility, we must solve the equation for y first.(x + 3)2 + ( y – 2)2 = 16

( y – 2)2 = 16 - (x + 3)2 y – 2 = ±y = 2 ±

To graph the circle you have to graph the top half in Y1.

Y1 = 2 + And the lower half in Y2.

Y2 = 2 – Be sure to use a square screen or the circle will appear distorted.

2)3(16 x

2)3(16 x

2)3(16 x

2)3(16 x

Circles

HomeworkPage 49 4 – 20 even, 36 - 48 even