Having trouble with circle problems

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I've been having a hard time with finding the equation from the center and the radius.
I did this one myself using the book to help, but I'm not sure if it's right.
Find the center of the circle whose equation is x2 + y2 – 3x + 8y – 8 = 0 (-3,8)?

These two are similar problems, so I guess I only need help with one.
Write the equation for the circle with the given center and radius.
Center (8, –4), radius 3

Find the equation of a circle centered at (–3, 3) having radius 4.
 
batbat said:
I've been having a hard time with finding the equation from the center and the radius.
I did this one myself using the book to help, but I'm not sure if it's right.
Find the center of the circle whose equation is x2 + y2 – 3x + 8y – 8 = 0 (-3,8)?
Complete the square on 'x' and 'y' separately.

x^2 + y^2 – 3x + 8y – 8 = 0
Rearrange
x^2 -3x + y^2 + 8y = 8
Complete the square on 'x'
x^2 -3x + ________ - _______ + y^2 + 8y = 8
(3)/2 = (3/2)
(3/2)^2 = 9/4
x^2 -3x + 9/4 - 9/4 + y^2 + 8y = 8
Simplify
[x - (3/2)]^2 + y^2 + 8y = 8 + 9/4
Complete the square on 'y'
[x - (3/2)]^2 + y^2 + 8y + _________ - _________= 8 + 9/4
(8)/2 = (4)
4^2 = 16
[x - (3/2)]^2 + y^2 + 8y + 16 - 16 = 8 + 9/4
Simplify
[x - (3/2)]^2 + (y+4)^2 = 8 + 9/4 + 16
Simplify
[x - (3/2)]^2 + (y+4)^2 = 105/4

Center (3/2,-4)
Radius ½*sqrt(105)

These two are similar problems, so I guess I only need help with one.
Write the equation for the circle with the given center and radius.
Center (8, –4), radius 3
Find the equation of a circle centered at (–3, 3) having radius 4.
These are a matter of knowing the right formulation, developed above. Eyeball problems, really. Just write it down.

Center (8, –4), radius 3

(x-8)^2 + (y+4)^2 = 3^2

circle centered at (–3, 3) having radius 4

(x+3)^2 + (y-3)^2 = 4^2

Really, that's all there is to it, once you see the form.

circle centered at (h,k) having radius r

(x-h)^2 + (y-k)^2 = r^2 -- Every time.
 
Wonderful, thanks so much, that helped a lot! I think I understand it better now.
 
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