Problem Solving

A student is drawing a friction drive in which two circular disks are in contact with each other. They are represented by circles in the drawing. The first has a radius of 10.0cm and the second has a radius of 12.0cm. What is the equation of each circle if the origin is at the center of the first circle and the x-axis passes through the center of the second circle?

Solution

First draw a sketch to help visualize the problem. Draw both circles and the x and y axes through the origin.

The equation of the first circle is: x^{2} + y^{2} = 10^{2}

The second circle is: (x – 22)^{2} + ( y – 0)^{2} = 12^{2}

or (x – 22)^{2} + y ^{2} = 144