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