To determine the scale factor between two circles, we compare their radii. Let's denote the radii of the two circles as follows:
- The radius of the first circle is [tex]\( x \)[/tex].
- The radius of the second circle is [tex]\( y \)[/tex].
The scale factor is essentially the ratio of the lengths of corresponding linear measurements of similar geometric figures. For circles, the radii can be used for this comparison.
The scale factor between the two circles is given by the ratio of their radii:
[tex]\[
\text{Scale Factor} = \frac{\text{Radius of the first circle}}{\text{Radius of the second circle}} = \frac{x}{y}
\][/tex]
Thus, the correct scale factor of the two circles, expressed as a fraction in its simplest form in terms of [tex]\( x \)[/tex] and [tex]\( y \)[/tex], is:
[tex]\[
\boxed{\frac{x}{y}}
\][/tex]
