A circle's center is at #(3 ,2 )# and it passes through #(5 ,8 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?

1 Answer
Deepak G.
Aug 14, 2016

Length of the Arc #=34.77#

Explanation:

Circle's center is at #(3,2)# and it passes through #(5,8)#
Therefore Length of the #radius=r# =Distance between these points#(3,2) and (5,8)#
or
#radius =r=sqrt((5-3)^2+(8-2)^2)#
#=sqrt(2^2+6^2)#
#=sqrt(4+36)#
#=sqrt40#
#=6.32#
Therefore Circumference of the Circle #=2pir=2pitimes6.32=39.74#
Arc covers #(7pi)/4# radians on the Circle
In other words Arc covers #(7pi)/4-:2pi=7/8times #(circumference of the Circle)
Therefore Length of the Arc #=7/8 times2pir=7/8 times39.74=34.77#

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