$\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{2}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{3}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-2)^2+(y-1)^2=3^2\implies (x-2)^2+(y-1)^2=9$

8 0

3 years ago

Circle X with a radius of 6 units and circle Y with a radius

asambeis [7]

Answer:

Option C.

Step-by-step explanation:

It is given that radius of circle X is 6 units and radius of circle Y is 2 units.

Here, circle Y is smaller and circle X is larger.

$\text{Scale factor}=\dfrac{\text{Radius of circle X}}{\text{Radius of circle Y}}$

$\text{Scale factor}=\dfrac{6}{2}$

$\text{Scale factor}=3$

If we translate the circles so they share a common center point, and after that we dilate circle Y by a scale factor of 3, then we get circle which is equal to circle X.

We know that, after dilation the figure and its image are similar.

Hence, we can say that both circles are similar.

Therefore, the correct option is C.

8 0

3 years ago