Three of the four vertices of a rectangle are (5,11), (16,11) and (16,-2). What is the area of the intersection of this rectangular region and the region inside the graph of the equation (x-5)^2 + (y+2)^2 =9? Express your answer as a common fraction in terms of .

Guest Dec 6, 2018

#1**+2 **

The center of the circle is on the 4rth corner of the rectangle (5, -2) and has radius of 3

1/4 of the circle is with in the rectangle

area of circle = pi r^2

1/4 of this = 1/4 pi (3)^2 = 9/4 pi = 7.068 sq units

ElectricPavlov
Dec 6, 2018

#2**+5 **

9pi /4

First, make you can make a good guess of what the missing point is by looking at the graph. (5,-2)

https://www.desmos.com/calculator

The you can see that a radius created here and the intersecting area is essentially an area of a sector, which (1/2) * (r^2) * the angle of the sector.

echofire18
Dec 6, 2018