Question

Using the following equation, find the center and radius of the circle.
x2 + 4x + y2 - 6y = -4

Answer 1

is this the equation?
$$\Large x^2 + 4x + y^2 -6y = -4 $$

Answer 2

yes

Answer 3

you can complete the square on x and y

Answer 4

can you explain this to me?

Answer 5

It is true that
$$ \Large x^2 + bx + \left( \frac b 2 \right) ^2 = \left(x+ \frac b 2 \right)^2 $$

Answer 6

can you verify this?

Answer 7

I have to complete the square and I'm not sure how to do that

Answer 8

that equation tells you how to complete the square. take the middle coefficient b, add (b/2) ^2

Answer 9

the coefficient of when the like terms are grouped

Answer 10

$$
x^2 + 4x + \color{red}{\left( \frac 4 2 \right)^2} + y^2 -6y+\color{blue}{\left( \frac {-6}{2} \right)^2} = -4+ \color{red}{\left( \frac 4 2 \right)^2}+ \color{blue}{\left( \frac {-6}{2} \right)^2}



$$

Answer 11

now use that identity above

Answer 12

$$
x^2 + 4x + \color{red}{\left( \frac 4 2 \right)^2} + y^2 -6y+\color{blue}{\left( \frac {-6}{2} \right)^2} = -4+ \color{red}{\left( \frac 4 2 \right)^2}+ \color{blue}{\left( \frac {-6}{2} \right)^2}

\\~\\
\large \left( x + \color{red}{\left( \frac 4 2 \right)}\right)^2 + \left( y +\color{blue}{\left( \frac {-6}{2} \right)}\right)^2 = -4+ \color{red}{\left( \frac 4 2 \right)^2}+ \color{blue}{\left( \frac {-6}{2} \right)^2}

$$

Answer 13

thank you i think i understand now