SOLUTION
Part A
Equation of a circle is given as
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{Where (h, k) are center cordinates and r = radius } \end{gathered}[/tex]
So for circle A, center (0, 0) and radius 6, the equation of the circle is
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-0)^2+(y-0)^2=6^2 \\ x^2+y^2=36 \end{gathered}[/tex]
For circle B, center (-4, -2) and radius 4, the equation of the circle is
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-(-4)^2+(y-(-2)^2=4^2 \\ (x+4)^2+(y+2)^2=16 \end{gathered}[/tex]
Making the graphs, we have
So the large green circle is for A and the smaller Blue circle is for B
Part B
The sequence of transformations that maps circle B unto circle A
We can see that circle B is smaller than circle A, that means circle B was derived from circle A being shrinked.
Now, from their radii, circle A is 6 units and circle B is 4 units. So the scale factor is
[tex]\frac{4}{6}=\frac{2}{3}[/tex]
So, the transformation a dilation; circle A was shrinked by a scale factor less than 1.
Also We can see that a shift was noticed. 4 units to the left and 2 units down.
Hence the answer is
The transformation is a dilation; circle A was shrinked by a scale factor less than 1 and was shifted 4 units to the left and 2 units down.
