Standard and General Form of the Circle's Equation?

Write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k).

(1) r = 3; (h, k) = (0, 0 )

(2) r = 5; (h, k) = (-5, 2)
asked Jan 16, 2013

(1) r = 3; (h, k) = (0, 0 )
General Form equation is x2 + y2 – 2hx – 2ky + h2 + k2 – r2 = 0, where (h, k) is the centre and r, the radius.
x2 + y2 + 2(0)x – 2(0)y + 02 + 02 – 32 = 0
x2 + y2 – 32 = 0
x2 + y2 – 9 = 0

Standard Form Equation is (x – h)2 + (y – k)2 = r2 where (h, k) is the centre and r, the radius.
(x – 0) 2 + (y – 0) 2 = 32
x2 + y2 = 9 .

2) r = 5; (h, k) = (-5, 2)
General Form equation is x2 + y2 – 2hx – 2ky + h2 + k2 – r2 = 0, where (h, k) is the centre and r, the radius.
x2 + y2 –2(–5)x – 2(2)y + (–5)2 + 22 – 52 = 0
x2 + y2 + 10x – 4y + 25 + 4 – 25 = 0
x2 + y2 + 10x – 4y + 4 = 0

Standard Form Equation is (x – h)2 + (y – k)2 = r2 where (h, k) is the centre and r, the radius.

(x – (–5)) 2 + (y–2)2 = 52
(x + 5)2 + (y – 2)2 = 25

answered Jan 16, 2013
selected Jan 23, 2013
Thank you!!! it helped a lot...