Find the equations of each of the circles in the figure (blue black and red) and calculate the shaded area.
Thank you for your help
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 . . .