Control-drag the equation of the circle.
Context Panel: Assign to a Name: C

Type the name C and press the Enter key.

Context Panel: Differentiate≻Implicitly
Set y as the dependent variable, remove y from the list of independent variables, and write $x\,x$ for "Differentiate with respect to".

Press the OK button in the dialog.

${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$

$-\frac{h^2-2xh+k^2-2yk+x^2+y^2}{-k^3+3y{k}^2-3y^{2}k+y^3}$

Using equation labels, write the expression for $\mathrm{\κ}$, then press the Enter key.

Context Panel: Simplify≻Assuming Real

Context Panel: Simplify≻With Side Relations
Enter C for Relations in the Specify Relations dialog, then click the OK button.

Control Panel: Simplify≻Assuming Positive

$\frac{\left|\frac{h^2-2xh+k^2-2yk+x^2+y^2}{k^3-3y{k}^2+3y^{2}k-y^3}\right|}{{\left(1+\frac{{\left(-x+h\right)}^2}{{\left(y-k\right)}^2}\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$

$\frac{1}{\sqrt{h^2-2xh+k^2-2yk+x^2+y^2}}$

$\frac{1}{\sqrt{r^2}}$

$\frac{1}{r}$