fan/medal to first person to help/answer
Using the following equation, find the center and radius:

x2 - 4x + y2 + 8y = -4 (5 points)

The center is located at (-2, -4), and the radius is 4.
The center is located at (2, -4), and the radius is 4.
The center is located at (-2, -4), and the radius is 16.
The center is located at (2, -4), and the radius is 16.

Question

fan/medal to first person to help/answer 
Using the following equation, find the center and radius:

x2 - 4x + y2 + 8y = -4 (5 points)
 	
	The center is located at (-2, -4), and the radius is 4.
	The center is located at (2, -4), and the radius is 4.
	The center is located at (-2, -4), and the radius is 16.
	The center is located at (2, -4), and the radius is 16.

campbell_st · Answer

well the general form of the circle you need is 

$$(x - h)^2 + (y - k)^2 = r^2$$

so you need to complete the square in both x and y...

can you do that..?

anonymous · Answer

what does k stand for and how do I find the height in the eqaution?

campbell_st · Answer

(h, k) is the centre of the circle and r is the radius

anonymous · Answer

okay so I need to find x first?

campbell_st · Answer

no you have 

$$x^2 - 4x $$

you need to add a value so it forms a perfect square  

e.g.$$(x - a)^2 = x^2 -2ax + a^2 $$

this is called completing the square..

ay thoughts...

campbell_st · Answer

so you need to compare 

2ax and 4x    any thoughts on the value of a...?

anonymous · Answer

im guessing 2

campbell_st · Answer

great  so 2^2 = 4 so add 4 to both sides of the equation to keep it in balance. 

now the equation can be written as 

$$(x - 2)^2 +y^2 + 8y = 0$$

next complete the square in y... 

$$(y + a)^2 =y^2 + 2ay + a^2 $$

so compare   2ay with 8y    what is the value of a..?

anonymous · Answer

4?

campbell_st · Answer

yes... so 4^2 = 16

again add 16 to both sides of the equation... and you get 

$$(x -2)^2 + (y + 4)^2 = 16$$

now you can identify the radius and centre

anonymous · Answer

is it D?

campbell_st · Answer

the expanded form of the equation, just to check is 

$$x^2 - 4x + 4 + y^2 _ 8y + 16 = 16  ~~or ~~x62 -4x + y^2 + 8y + 20 = 16$$

subtract 20 from both sides of the equation and you get

$$x^2 -4x + y^2 + 8y = -4$$

the original equation

campbell_st · Answer

no it's not... remember the equation is 

$$(x - h)^2 + (y - k)^2 = r^2$$

(h, k) is the centre r is the radius... so take the square root to find r

campbell_st · Answer

the centre is correct..

anonymous · Answer

r=4?

campbell_st · Answer

that's correct

now you have all the information you need

anonymous · Answer

so B is the correct answer correct?

campbell_st · Answer

that's correct

anonymous · Answer

you're awesome!

anonymous · Answer

i would fsn u but i already am