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.

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Presentation transcript:

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

The 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:

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).

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

Graphing Circles Graph 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 Circles To 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 Y 1. Y 1 = 2 + And the lower half in Y 2. Y 2 = 2 – Be sure to use a square screen or the circle will appear distorted.

Circles Homework Page 49 4 – 20 even, even