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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