Tools≻Load Package: Student Precalculus

Control-drag the equation of the circle and press the Enter key.

Context Panel: Differentiate≻Implicitly
In the dialog that appears (see Figure 2.4.2(a)), set $y$ as the dependent variable and $x$ as the independent variable. Write $x$ in the "Differentiate with respect to" box.

Reference the equation of the circle by its equation label and press the Enter key.

Context Panel: Differentiate≻Implicitly
Write $x\,x$ in the "Differentiate with respect to" box. (See Figure 2.4.2(a).)

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

$-\frac{h^2-2hx\+k^2-2ky\+x^2\+y^2}{-k^3\+3k^{2}y-3k{y}^2\+y^3}$

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

Context Panel: Simplify≻Assuming Real

Context Panel: Student Precalculus≻Complete the Square≻Designated Quantities≻$\left[x\,y\right]$ 

Context Panel: Simplify≻With Side Relations≻$C$

Context Panel: Simplify≻Assuming Positive

$\frac{\left|\frac{h^2-2hx\+k^2-2ky\+x^2\+y^2}{-k^3\+3k^{2}y-3k{y}^2\+y^3}\right|}{{\left(1\+\frac{{\left(-x\+h\right)}^2}{{\left(y-k\right)}^2}\right)}^{3\/2}}$

$\frac{\left|h^2-2hx\+k^2-2ky\+x^2\+y^2\right|}{{\left(h^2-2hx\+k^2-2ky\+x^2\+y^2\right)}^{3\/2}}$

$\frac{\left|{\left(x-h\right)}^2\+{\left(y-k\right)}^2\right|}{{\left({\left(x-h\right)}^2\+{\left(y-k\right)}^2\right)}^{3\/2}}$

$\frac{{\left|r\right|}^2}{{\left(r^2\right)}^{3\/2}}$

$\frac{1}{r}$

Define the circle.

Apply the implicitdiff and simplify commands.

Apply the CompleteSquare command from the Student Precalculus package.

Apply the simplify command with $C$ as a side relation.

Apply the simplify command.