# Thread: Conics Circle Super simple question

1. ## Conics Circle Super simple question

Given the following:

x^2+y^2-6y+4x-16=0

how do I find the measure of the radius?

2. $\displaystyle x^2+y^2-6y+4x-16=0$

$\displaystyle (x+2)^2+(y-3)^2=29$

Obviously, the radiius is $\displaystyle \sqrt{29}$

ALITER:

The general equation of a circle is
$\displaystyle x^2+y^2+2gx+2fy+c=0$
the centre being $\displaystyle (-g,-f)$ and the $\displaystyle radius=\sqrt{g^2+f^2-c}$

As per your question $\displaystyle g=2,f=-3,c=-16$
Therefore
$\displaystyle radius=\sqrt{2^2+(-3)^2-(-16)}=\sqrt{29}$

3. Can you elaborate on/explain the steps involved between:

x^2+y^2-6y+4x-16=0
and
(x+2)^2+(y-3)^2=29

4. Originally Posted by s3a
Can you elaborate on/explain the steps involved between:

x^2+y^2-6y+4x-16=0
and
(x+2)^2+(y-3)^2=29

Are you familiar with completing the square?

$\displaystyle x^{2} + y^{2} - 6y + 4x - 16 = 0$
Rearrange terms:
$\displaystyle x^{2} + 4x + y^{2} - 6y = 16$
Complete the square:
$\displaystyle x^{2} + 4x + 4 + y^{2} - 6y + 9 = 16 + 4 + 9$
Factor and simplify:
$\displaystyle (x + 2)^{2} + (y - 3)^{2} = 29$

01

5. In the "Completing the Square" step, how did you make 4 and 9 randomly appear? I understand how you need it on both sides but I don't understand how you "created" them.

6. You can "create" anything in one side of the equation as long as your create the same thing on the other side. So, 4 and 9 were added to the left side of the equation so that the square could be completed, but they had to also be added to the right side to balance things out.

7. But why 4 and 9? Why not other numbers?

8. Originally Posted by s3a
But why 4 and 9? Why not other numbers?
Because they 'complete the square'. You were asked earlier .... Are you familiar with completing the square? If not, then you need to go back and review this technique. Use Google to find appropriate rsources if your class notes or textbook don't have it.