Question

What the center and radius of this circle from this equation? x^2 + 2x + y^2 + 4y = 20

Answer 1

I will give a medal to the correct answer.

Answer 2

\(\large\color{slate}{ x^2 + 2x \color{red}{+1}~+~ y^2 + 4y \color{blue}{+4}= 20~\color{red}{+1}~\color{blue}{+4} }\)

Answer 3

each of the underlined from the following is a perfect square:
\(\large\color{slate}{ \underline{x^2 + 2x \color{red}{+1}~}+~ \underline{~y^2 + 4y \color{blue}{+4}~}= \underline{~20~\color{red}{+1}~\color{blue}{+4}~} }\)

Answer 4

Still don't understand how to get the center and radius from this?

Answer 5

first extract the equation of a circle in a vertex form, then we will deal with finding radius and center

Answer 6

\(\large\color{slate}{ \underline{x^2 + 2x \color{red}{+1}~}+~ \underline{~y^2 + 4y \color{blue}{+4}~}= \underline{~20~\color{red}{+1}~\color{blue}{+4}~} }\)
\(\large\color{slate}{\Downarrow }\) \(\large\color{slate}{\Downarrow }\) \(\large\color{slate}{\Downarrow }\)
\(\large\color{slate}{ \underline{(x+1)^2}~~+~~~ \underline{~~~~~~?~~~~~}~~~~~=~~~~ \underline{~~~~~~?~~~~~~} }\)

Answer 7

what will it be in a vertex form ?