Answer:
Center: (1,3)
Radius: 6
Step-by-step explanation:
Hi there!
Typically, the equation of a circle would be in the form where
is the center and
is the radius.
To get the given equation into this form, we must complete the square for both x and y.
<u>1) Complete the square for x</u>
Let's take a look at this part of the equation:
To complete the square, we must add to the expression the square of half of 2. That would be 1² = 1:
Great! Now, let's add this to our original equation:
We cannot randomly add a 1 to just one side, so we must do the same to the right side of the equation:
Complete the square:
<u>2) Complete the square for y</u>
Let's take a look at this part of the equation :
To complete the square, we must add to the expression the square of half of 6. That would be 3² = 9:
Great! Now, back to our original equation:
Remember to add 9 on the other side as well:
Complete the square:
<u>3) Determine the center and the radius</u>
Now, we can see that (1,3) is in the place of (h,k). 36 is also in the place of r², making 6 the radius.
I hope this helps!