Circle and Radius, having to complete the square?

• Sep 11th 2012, 03:48 PM
Chaim
Circle and Radius, having to complete the square?
Hi, I have this problem where I am supposed to find the circle and radius.
Here is what I did and the steps (click on the picture to enlarge it)
Attachment 24771
And I'm stuck at this part.
I think I am supposed to be using 'completing the square' here right?
But can someone explain to me how to do that?

Because after that, I'm able to find the center, which is (h,k)
Then the radius would be the square root of the number that comes at the other end.

Thanks :)
• Sep 11th 2012, 05:01 PM
HallsofIvy
Re: Circle and Radius, having to complete the square?
Yes, complete the square. $4x^2+ 8x= 4(x^2+ 2x)$. Now what do you have to add to make $x^2+ 2x+ ?$ a perfect square. You should already know that $(x+ a)= x^2+ 2ax+ a^2$. So if 2a= 2, what is a? And then what is $a^2$?

Similarly, $4y^2+ 24y= 4(y^2+ 6y)$. Now compare $y^2+ 6y$ to $y^2+ 2ay+ a^2$. If 2a= 6, what is a? What is $a^2$?
• Sep 11th 2012, 05:02 PM
skeeter
Re: Circle and Radius, having to complete the square?
$4x^2+4y^2+8x=-24y+39$

divide every term by 4 ...

$x^2+y^2+2x = -6y + \frac{39}{4}$

re-arrange ...

$x^2+2x+y^2+6y= \frac{39}{4}$

complete the square for x and y ...

$x^2+2x+1+y^2+6y+9= \frac{39}{4}+10$

$(x+1)^2 + (y+3)^2 = \frac{79}{4}$
• Sep 11th 2012, 05:54 PM
Chaim
Re: Circle and Radius, having to complete the square?
Ah I see ok thanks!
So basically it's like the tic tac toe method (if you guys heard of it), where you basically find numbers that would fit in.

Ok thanks! :)