the equation of a circle in expanded form is shown. what is the equation of the circle in standard form? use…

Explanation:

Step1: Group x - terms and y - terms

$(x^{2}-8x)+(y^{2}+4y)-16 = 0$

Step2: Complete the square for x - terms

For $x^{2}-8x$, we add $(\frac{-8}{2})^2=16$ inside the parentheses. $(x^{2}-8x + 16)+(y^{2}+4y)-16-16=0$ $(x - 4)^{2}+(y^{2}+4y)-32 = 0$

Step3: Complete the square for y - terms

For $y^{2}+4y$, we add $(\frac{4}{2})^2 = 4$ inside the parentheses. $(x - 4)^{2}+(y^{2}+4y+4)-32 - 4=0$ $(x - 4)^{2}+(y + 2)^{2}=36$ $(x - 4)^{2}+(y + 2)^{2}=6^{2}$

Answer:

$(x - 4)^{2}+(y + 2)^{2}=6^{2}$