Circles and their equations

Question

Three gears A, B, C mesh with each other in a motor assembly.  Gear A has a radius of 4 in., gear B has a radius of 3 in., and gear C has a radius of 1 in.  The largest gear is centered at (-7, 0), the smallest gear at (4, 0), and the other gear at (0, 0).

What is the equation of each gear?

Graph the equations.

Answer 1

For gear A:

Center (-7,0) ,Radius 4 in

General equation of the circle: (x-h)²+(y-k)² =r²:Center (h , k) ,Radius r

(x-(-7))²+(y-0)² =4²

(x+7)²+y² =16     -----For gear A

For gear B:

Center (0,0) ,Radius 3 in

General equation of the circle: (x-h)²+(y-k)² =r²:Center (h , k) ,Radius r

(x-0)²+(y-0)² =3²

x²+y² =9     ----- For gear B

For gear C:

Center (4,0) ,Radius 1 in

General equation of the circle: (x-h)²+(y-k)² =r²:Center (h , k) ,Radius r

(x-4)²+(y-0)² =1²

(x-4)²+y² = 1     ----- For gear C

Comments

updated graph please check