Question
Find the area of the region that lies outside the circle x^2 + y^2 = 4 but inside the circle x^2 + y^2 -6 x -16 = 0.
Answers
mathhelper
x^2 + y^2 -6 x -16 = 0
x^2 - 6x + 9 + y^2 = 16+9
(x-3)^2 + y^2 = 25
centre at (3,0), radius 5
x^2 + y^2 = 4
centre at (0,0), radius 2
a quick sketch will show that the smaller circle lies entirely inside the larger
and they have a common point at (-2,0)
So all we need is the area of the larger - area of the smaller
= 25π - 4π square units
= 21π square units
x^2 - 6x + 9 + y^2 = 16+9
(x-3)^2 + y^2 = 25
centre at (3,0), radius 5
x^2 + y^2 = 4
centre at (0,0), radius 2
a quick sketch will show that the smaller circle lies entirely inside the larger
and they have a common point at (-2,0)
So all we need is the area of the larger - area of the smaller
= 25π - 4π square units
= 21π square units