To find the ratio of the radii of the two circles, let's go through the problem step-by-step:
1. Identify the diameters of the circles:
- The diameter of the first circle is given by [tex]\( 12x \)[/tex].
- The diameter of the second circle is given by [tex]\( 6x^2y \)[/tex].
2. Calculate the radii:
- The radius of the first circle is half of its diameter.
[tex]\[
\text{Radius of the first circle} = \frac{12x}{2} = 6x
\][/tex]
- Similarly, the radius of the second circle is half of its diameter.
[tex]\[
\text{Radius of the second circle} = \frac{6x^2y}{2} = 3x^2y
\][/tex]
3. Determine the ratio of the radii:
- To find the ratio of the radii of the first circle to the second circle, we divide the radius of the first circle by the radius of the second circle.
[tex]\[
\text{Ratio of the radii} = \frac{6x}{3x^2y} = \frac{6x}{3x^2y} = \frac{6}{3xy} \cdot \frac{1}{x} = \frac{2}{xy}
\][/tex]
Thus, the ratio of the radii of the two circles is [tex]\( \frac{2}{xy} \)[/tex].
However, this doesn't directly match any of the given options. We need to reinterpret the available options to find the correct match. Given the choices:
```plaintext
A) 2x^3y
B) 2xy
C) x \cdot 2y
D) 2: xy (which means [tex]\( \frac{2}{xy} \)[/tex])
```
The correct answer, in matching form, is:
[tex]\[ \boxed{2: xy} \][/tex]
