Section 2.2 class notes_0

# Section 2.2 class notes_0 - 2.2.9 Write the equation in...

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( , ) h k k h r Section 2.2 Circles A circle is the set of all points ( , ) x y in the Cartesian plane that are a fixed distance r from a fixed point ( , ) h k . The fixed distance r is called the radius of the circle and the fixed point ( , ) h k is called the center of the circle. To derive the equation of a circle, we use the distance formula that was discussed in the previous section. A circle with center ( , ) h k and radius r The standard form of an equation of a circle with center ( , ) h k and radius r is ( 29 ( 29 2 2 2 x h y k r - + - = . The standard form of an equation of a circle centered at the origin with radius r 2 2 2 x y r + = . Objective 1 : Writing the Standard Form of an Equation of a Circle Note that we can use the midpoint formula to determine the center of a circle given the endpoints of a diameter of the circle. The radius can be found using the distance formula. 2.2.7 Find the standard form of the equation of the circle with endpoints of a diameter at the points _____ and _____.

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Unformatted text preview: 2.2.9 Write the equation in standard form for a circle with center ______ and tangent to the x-axis. Objective 2 : Sketching the Graph of a Circle Once we know the center and radius of a circle, we can easily graph the circle. For additional points, find any intercepts and plot the points. Note that the y-coordinate of the center of the circle ( 29 ( 29 2 2 1 2 9 x y-+ + = ( 2 k = -) is negative because ( 29 ( 29 2 2 2 ( 2) . y y + =- -Objective 3 : Converting the General Form of a Circle into Standard Form The general form of the equation of a circle is 2 2 Ax By Cx Dy E + + + + = where , , , ,and A B C D E are real numbers and . A B = By completing the square, the equation of a circle can be rewritten from general form to standard form. 2.2.25 Find the center, radius, and intercepts of the circle with the given equation and then sketch the graph....
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## This note was uploaded on 09/08/2011 for the course MATH 1001 taught by Professor Moshe during the Spring '09 term at LSU.

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Section 2.2 class notes_0 - 2.2.9 Write the equation in...

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