Answer:
See below.
Step-by-step 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:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
Plugging the numbers in, we get:
[tex](x-(-4))^2+(y-3)^2=3^2[/tex]
[tex](x+4)^2+(y-3)^2=9[/tex]
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:
[tex](x+4)^2+(y-3)^2=15^2[/tex]
Thus, equation for the fourth circle is:
[tex](x+4)^2+(y-3)^2=225[/tex]
