UNIT 8 - OBJECTIVE 1 - THE CIRCLE

		A circle is the set of all points in a plane that are at the same fixed 
		distance from a fixed point in the plane. The fixed point is called 
		the center of the circle and the fixed distancce is called radius.
		The equation of a circle with center at the origin and radius r is
		

		The equation of the circle with center (h,k) and radius r is
		


		EXAMPLE 1
		Describe the graph  and graph the circle
		x-3=x-h				y-k=y+4					
		So 3=h				So k=-4


		So the center of the circle is (3,-4)  and the radius is 3.
		
		EXAMPLE 2
		Find the equation of the circle whose center is (0,2) and radius =2.
		


		EXAMPLE 3
		Find the equation of the circle whose center is (-1,4) and which goes through the 
		point (-2,3).

		We need to find the distance between (-1,4) and (-2,3) because this is the radius
		

		So the equation is
		


		EXAMPLE 4
		Find the center and radius of the circle and graph:
		

		We need to complete the square to find the center and radius.
		Put the constant on the right and put x and y terms together 
		

		Because coefficients of  are one complete the square by adding
		 to both sides.


		
		
So the center is (2,3) and the radius is 5.

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