Question

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)

Answer 1

(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

 

source: http://answers.yahoo.com/question/index?qid=20071125073022AADwDqu

Comments

Thank you!!! it helped a lot...