Question

when you make the circle bigger or smaller which number of the standard equation for a circle centered at the orgin changes

Answer 1

To dilate a circle by a determined scale factor k you have to work on the standard equation of the circle

$x^2+y^2=r^2$

You have to multiply the radius by the squared scale factor:

$x^2+y^2=k^2r^2$

So, if do example you want to dilate a circle by a scale factor 3, you have to multiply the radius by the square of 3

$\begin{gathered} k=3 \\ 3^2=9 \end{gathered}$

The formula of the circle dilated by k=3 is

$x^2+y^2=9r^2$