UNIT 8 - OBJECTIVE 1 - THE CIRCLE
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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.