Question

Would you be able to help me come up with an equation like the one shown in the picture? :)

Answer 1

Given the equation

`\begin{gathered} x^2+y^2+4x-4y-17=0 \\ (x^2+4x+k)+y^2-4y+p)=17+k+p \\ k=((4)/(2))^2=2^2=4 \\ p=(-(4)/(2))^2=4 \end{gathered}`
`\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}`
`\begin{gathered} Thus,\text{ the standard form of the equation of the circle is } \\ (x+2)^(2)+(y-2)^(2)=5^(2) \end{gathered}`

A similar equation like the one shown in the picture is given below

`\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}`