The Solution:
Given the properties:
Circle A:
[tex]\begin{gathered} \text{ Center(a,b)=(}0,0) \\ \text{ radius r=6} \end{gathered}[/tex]
By the formula for the equation of a circle,
[tex](x-a)^2+(y-b)^2=r^2[/tex]
But
[tex]a=0,b=0,r=6[/tex]
Substituting, we get
[tex]\begin{gathered} (x-0)^2+(y-0)^2=6^2 \\ x^2+y^2=6^2 \end{gathered}[/tex]
For Circle B:
[tex]\begin{gathered} \text{ Center(a,b)=(-4,-2)} \\ \text{ radius r=4} \end{gathered}[/tex]
Substituting these values in the formula for the equation of a circle.
[tex]\begin{gathered} (x--4)^2+(y--2)^2=4^2 \\ (x+4)^2+(y+2)^2=4^2 \end{gathered}[/tex]
Graphing the two circles using the Desmos graph plotter, we have
Part B:
The transformation is a dilation by a scale factor of 4/6 (a shrink of circle A) and was shifted by 4 units left and 2 units down.
Part C:
The mapping shows that circle B is a shrink of circle A.
Circle A has its center at the origin (0,0) while the center of circle B is at (-4,-2)
