Solution
Given the equation
[tex]\begin{gathered} x^2+y^2+4x-4y-17=0 \\ (x^2+4x+k)+y^2-4y+p)=17+k+p \\ k=(\frac{4}{2})^2=2^2=4 \\ p=(-\frac{4}{2})^2=4 \end{gathered}[/tex][tex]\begin{gathered} (x^2+4x+4)+(y^2-4y+4)=17+4+4 \\ Factorize \\ (x+2)^2+(y-2)^2=25 \\ (x+2)^2+(y-2)^2=5^2 \\ \end{gathered}[/tex][tex]\begin{gathered} Thus,\text{ the standard form of the equation of the circle is } \\ (x+2)^{2}+(y-2)^{2}=5^{2} \end{gathered}[/tex]
A similar equation like the one shown in the picture is given below
[tex]\begin{gathered} Expanded\text{ form:} \\ x^2-6x+y^2+8y-11=0 \\ General\text{ form} \\ \left(x-3\right)^2+\left(y+4\right)^2=36 \end{gathered}[/tex]
