Question

If a graphic designer is drawing a pattern of four concentric circles on a coordinate plane. The center of the circles is located at (-4, 3). The smallest circle has a radius of 3 units. If the radius of each circle is 4 units greater than the largest circle within it, then the equation of the fourth circle is...

Answer 1

See below.

Explanation:

Let's first find the equation of the smallest circle. We know the center is at (-4,3) and the radius is 3 units. Recall the equation for a circle:

`(x-h)^2+(y-k)^2=r^2`

Where (h,k) is the center and r is the radius.

Plugging the numbers in, we get:

`(x-(-4))^2+(y-3)^2=3^2`

`(x+4)^2+(y-3)^2=9`

Each subsequent circle's radius is 4 units greater than the smallest circle. Importantly, note that the center will remain unchanged. The largest circle will have a radius of 3 + 4 + 4 + 4 = 15. We simply need to change the r:

`(x+4)^2+(y-3)^2=15^2`

Thus, equation for the fourth circle is:

`(x+4)^2+(y-3)^2=225`