Posted by **rmz** on Friday, February 19, 2010 at 5:39pm.

Garden Area Problem. A designer created a garden

from two concentric circles whose equations are as follows:

(x+2)^2+(y-6)^2=16 and (x+2)^2+(y-6)^2=81

The area between the circles will be covered with grass. What is the area of that section?

How do you do this?

- Math -
**MathMate**, Friday, February 19, 2010 at 7:56pm
The equation of a standard circle with centre at (a,b) and radius r is

(x-a)² + (y-b)² = r²

By inspection of the given circle,

(x+2)^2+(y-6)^2=16 and (x+2)^2+(y-6)^2=81

we conclude that both have centres at (-2,6), therefore they are concentric.

The radii of the circles are √16=4 and √81=9.

The area between the two circles are therefore

πr1²-πr2²

=π(9²-4²)

=65π

- Math -
**rmz**, Friday, February 19, 2010 at 8:13pm
do you have any sites that explain this as well?

- Math -
**MathMate**, Friday, February 19, 2010 at 8:25pm
The subject should be in any pre-calc textbook. Alternatively, you can google

"equation of a circle".

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