A. find the equation of both circles b. Find the area of both circles c. Find the area of the shaded origin

Question

The small circle is tangent internally at (-2,0) to a big circle. The center of the small circle coincides with the origin and the big circle passes through (6,0)

Answer 1

The small circle is inside the big circle.  That have a common point of (-2, 0).  The centerpoint of the small circle is the origin.

 

The equation of the smaller circle is

 

x² + y² = 4

 

 

Now we get the equation of the larger circle.

 

This circle will stretch from (-2, 0) to (6, 0).  This means that the centerpoint is on the x axis.  We use these point to find the centerpoint and radius.

 

If take the average between the two x coordinate, we get the x-coordinate of the centerpoint.  That x-coordinate is 2.  So the centerpoint is (2, 0).  Then we get the radius.

 

r = 6 - 2 = 4

 

 

Therefore, the equation of the larger circle is

 

(x - 2)² + y² = 16