The circle equation is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where the center is at point (h,k) and the radius is r.
For circle O, we get
[tex]\begin{gathered} (x+2)^2+(y-7)^2=5^2 \\ (x+2)^2+(y-7)^2=25 \end{gathered}[/tex]
and for circle P, we have
[tex]\begin{gathered} (x-12)^2+(y+1)^2=12^2 \\ (x-12)^2+(y+1)^2=144 \end{gathered}[/tex]
Now, in order to obtain circle P from circle O, we need 2 translations and 1 expansion, that is,
we must translate the center of circle O at (-2,7) 14 units right and 8 units down and get the center of circle P at (12,-1).
These translatiions are given by
[tex]\begin{gathered} (h,k)\Rightarrow(h+14,k) \\ \text{and} \\ (h+14,k)\Rightarrow(h+14,k-8) \end{gathered}[/tex]
where (h,k)=(-2,7). By doing these tranlastions, we get
Finally, in order to get the circle P, we need to stretch the radius from r=5 to r=12, this transformation is given by
[tex]r=5\Rightarrow r=12[/tex]
which give us circle P (blue circle in the last picture)
