# Find the center and radius of a circle?

• Dec 1st 2012, 10:21 AM
M670
Find the center and radius of a circle?
Find the coordinates of the center and the radius of the circle given by the equation $\displaystyle y(y-4)+x(x+3)=0$
I know $\displaystyle (h,k)$ is the center which if I am right its $\displaystyle (4,-3)$ but how do I find the radius ?
if I take $\displaystyle y(y-4)+x(x+3)=0$ and expand it out to $\displaystyle y^2-4y+x^2+3x=0$ how do I enter that into $\displaystyle (x-h)^2+(y-k)^2=r^2$ Because I think I need to find atleast one coordinate to find my radius?
• Dec 1st 2012, 11:01 AM
earboth
Re: Find the center and radius of a circle?
Quote:

Originally Posted by M670
Find the coordinates of the center and the radius of the circle given by the equation $\displaystyle y(y-4)+x(x+3)=0$
I know $\displaystyle (h,k)$ is the center which if I am right its $\displaystyle (4,-3)$ but how do I find the radius ?
if I take $\displaystyle y(y-4)+x(x+3)=0$ and expand it out to $\displaystyle y^2-4y+x^2+3x=0$ how do I enter that into $\displaystyle (x-h)^2+(y-k)^2=r^2$ Because I think I need to find atleast one coordinate to find my radius?

1. You've done the first step:

$\displaystyle y(y-4)+x(x+3)=0$ expands to $\displaystyle y^2-4y+x^2+3x=0$

2. Now complete the square(s):

$\displaystyle y^2-4y+4+x^2+3x+\left(\frac32 \right)^2=4+\left(\frac32 \right)^2$

$\displaystyle \left(x+\frac32 \right)^2 + \left(y-2 \right)^2=\frac{25}4 = \left(\frac52 \right)^2$

3. Thus the midpoint of the circle is $\displaystyle M\left(-\frac32 , 2 \right)$ and the radius is $\displaystyle r = \frac52$
• Dec 1st 2012, 11:10 AM
M670
Re: Find the center and radius of a circle?
Quote:

Originally Posted by earboth
1. You've done the first step:

$\displaystyle y(y-4)+x(x+3)=0$ expands to $\displaystyle y^2-4y+x^2+3x=0$

2. Now complete the square(s):

$\displaystyle y^2-4y+4+x^2+3x+\left(\frac32 \right)^2=4+\left(\frac32 \right)^2$

$\displaystyle \left(x+\frac32 \right)^2 + \left(y-2 \right)^2=\frac{25}4 = \left(\frac52 \right)^2$

3. Thus the midpoint of the circle is $\displaystyle M\left(-\frac32 , 2 \right)$ and the radius is $\displaystyle r = \frac52$

Thank You, I was missing my step of completing the squares