SOLUTION: This is a three part question. I wasn't too sure where to post it, so I posted the question here. Given the equation of the circle, label the center and radius of the circle. A

You must get these in the standard form
for a circle



Then the center is (h,k) and the radius is r.

A)  



Get the constant term on the right by
adding  to both sides:



Multiply the coefficient of ,
which is  by , getting
. Then square ,
getting  and add to
both sides, putting it right after the
 on the left:



Factor the first three terms on the left,
and combine the numbers on the right



And write  as 



Multiply the coefficient of ,
which is  by , getting
.  Then square ,
getting  and add to
both sides, putting it right after the
 on the left:



Factor the last three terms on the left,
and combine the numbers on the right



And write  as 



and write  as 

, which we compare to

, and so

since  then , and

since  then , and 

so the center is (h,k) = (-1,-5) and the radius is r=7.




B)  

Exactly the same way:

The constant term is already on the right,
so we don't have to get it over there.

Multiply the coefficient of ,
which is  by , getting
. Then square ,
getting  and add to
both sides, putting it right after the
 on the left:



Factor the first three terms on the left,
and combine the numbers on the right



And write  as 



Multiply the coefficient of ,
which is  by , getting
.  Then square ,
getting  and add to
both sides, putting it right after the
 on the left:



Factor the last three terms on the left,
and combine the numbers on the right



And write  as 



and write  as 

, which we compare to

, and so

since  then , and

since  then , and 

so the center is (h,k) = (-2,6) and the radius is r=8.


C) 

This is just like the other except it'e a little
easier because we don't have to complete the square 
of y because there is no term in y, so we do something 
else there. But we begin the same way:



Get the constant term on the right by
adding  to both sides:



Multiply the coefficient of ,
which is  by , getting
. Then square ,
getting  and add to
both sides, putting it right after the
 on the left:



Factor the first three terms on the left,
and combine the numbers on the right



And write  as 



Now the only thing we have to do is write the
term  as 

 

Then write the 36 on the right as 

, which we compare to

, and so

since  then , and

since  then , and 

so the center is (h,k) = (5,0) and the radius is r=6.

Now be sure to learn how to do this by practicing on

some other problems like these, because even though I

can do your homework for you, I can't pass your tests

that you take in class for you, and your homework won't 

do you any good if you flunk the tests, because your 

teacher will then know you just got somebody to do your 

homework for you.

Edwin