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Lesson35 - Lesson 35 MA 15200 Section 2.8 A circle is a set...

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Lesson 35 MA 15200, Section 2.8 A circle is a set of all points in a plane that are a fixed distance, called the radius , and from a point called its center. Equation of a circle: The distance formula can be used to find the equation of a circle. Let the center of the circle be represented by the ordered pair ( h, k ) and the radius of the circle by r . Every point ( x, y ) is r units from ( h, k ). 2 2 2 2 2 ) ( ) ( ) ( ) ( k y h x r k y h x r - + - = - + - = This is the standard equation for a circle. Standard Equation of a Circle: If the center of a circle is ( h, k ) and the radius of the circle is r units, the an equation for the circle is 2 2 2 ) ( ) ( r k y h x = - + - . If the center of the circle is the origin, then the standard equation of the circle is 2 2 2 r y x = + . The general equation for a circle is an equation where the parentheses are cleared from the standard form (binomials are squared) . General Equation of a Circle: numbers. real represent and , , where , 0 2 2 e d c e dy cx y x = + + + + Ex 1: Find the standard equation and general form of each circle described.
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