Find the equations of each of the circles in the figure (blue black and red) and calculate the shaded area.

http://img.photobucket.com/albums/v3...t_coco/1-1.jpg

Thank you for your help

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- Jan 15th 2008, 06:34 PMlemonteaHelp! Urgent Circle question
Find the equations of each of the circles in the figure (blue black and red) and calculate the shaded area.

http://img.photobucket.com/albums/v3...t_coco/1-1.jpg

Thank you for your help - Jan 15th 2008, 06:49 PMSoroban
Hello, lemontea!

This is straight-forward.

Exactly where is your difficulty?

The blue circle has center (0,0) and radius 4: .$\displaystyle x^2 + y^2 \:=\:16$

The red circle has center (0,2) and radius 2: .$\displaystyle x^2 + (y-2)^2 \:=\:4$

The black circle has center (0,-2) and radius 2: .$\displaystyle x^2 + (y+2)^2\:=\:4$

The shaded region is the area of the blue circle

. . minus the areas of the red and black circles.

Surely you know how to find the area of a circle . . .