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Section 2-1.8

# Section 2-1.8 - through the center is called the diameter...

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2.8 – Distance and Midpoint Formulas; Circles The distance between any two points can be found using the formula 2 1 2 2 1 2 ) ( ) ( y y x x d ! " ! # . ! Example 1 Given the two points (-4,9) and (1,-3), find the distance between them. " The midpoint of the line segment from ) , ( 1 1 y x to ) , ( 2 2 y x can be found using the formula \$ % & ( ) " " 2 , 2 2 1 2 1 y y x x . ! Example 2 Given a line segment with endpoints at (1,2) and (7,-3), find the midpoint. "

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An application that involves both the distance and the midpoint is the circle . A circle is the set of all points in a plane that are equidistant from a fixed point called the center . The fixed distance from the circle’s center to any point on the circle is called the radius . A line segment drawn from a point to another point on the opposite side of the circle that passes
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Unformatted text preview: through the center is called the diameter . The center is the midpoint of every diameter line segment. Equations of Circles Assume that the circle has a center at ) , ( k h and a radius equal to r . 1. General Form: 2 2 # &amp;quot; &amp;quot; &amp;quot; &amp;quot; F Ey Dx y x 2. Standard Form: 2 2 2 ) ( ) ( r k y h x # ! &amp;quot; ! Use completing the square to convert from general form to standard form. ! Example 3 Given the equation 16 ) 2 ( ) 1 ( 2 2 # ! &amp;quot; &amp;quot; y x , find the center and radius. Sketch the graph. &amp;quot; ! Example 5 Given the equation of the circle 4 6 12 2 2 # ! ! &amp;quot; &amp;quot; y x y x , find the center and radius. &amp;quot;...
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