Question

Three gears of radii 6 in., 4 in., and 2 in. mesh with each other in a motor assembly as shown to the right. What is the equation of each circle in standard form?
*How can the diagram of the gears in the coordinate plane help you solve this problem?
*How can you write an equation for each circle?

Answer 1

Find the coordinates of the center of each circle.
Then the equation of the circle is: (x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center and r is the radius.

Answer 2

Okay, so the coordinates of each circle is (0,0) (8,6) and (8,0)

Answer 3

@aum pls help

Answer 4

circle centered at (0,0) has radius 6: x^2 + y^2 = 6^2 = 36

Answer 5

Circle centered at (8,6) has radius 4: x^2+y^2=

Answer 6

Wouldn't the equation be (x-8)^2+(y-6)^2=r^2

Answer 7

(x-8)^2+(y-6)^2=4^2
(x-8)^2+(y-6)^2=16

Answer 8

circle centered at (0,0) has radius 6: (x-0)^2 + (y-0)^2 = 6^2
x^2 + y^2 = 36

circle centered at (8,6) has radius 4: (x-8)^2 + (y-6)^2 = 4^2
(x-8)^2 + (y-6)^2 = 16

circle centered at (8,0) has radius 2: (x-8)^2 + (y-0)^2 = 2^2
(x-8)^2 + y^2 = 4

Answer 9

Can you help with the last question of this problem?

Answer 10

what is it?

Answer 11

We just wrote the equations of the three circles and the last question asks for them.

Answer 12

I thought that was for the first question?

Answer 13

I don't know why these questions are backwards.

Answer 14

*How can the diagram of the gears in the coordinate plane help you solve this problem?
The diagram in the coordinate plane helps locate the center of each circle fairly easily.

*How can you write an equation for each circle?
There is a standard equation for a circle with center at (h, k) and radius r. It is:
(x-h)^2 + (y-k)^2 = r^2
Once we know the coordinates of the center of the circle we know h and k. The radius of the circle 'r' is given to us. So we plug in h, k and r into the standard equation of the circle to get the equation for each circle.