A circle's center is at #(2 ,4 )# and it passes through #(3 ,1 )#. What is the length of an arc covering #(13pi ) /8 # radians on the circle?

1 Answer
Deepak G.
Aug 16, 2016

Length of the Arc #=16.14#

Explanation:

Circle's center is at #(2,4)# and it passes through #(3,1)#
Therefore Length of the #radius=r# =Distance between these points#(2,4) and (3,1)#
or
#radius =r=sqrt((3-2)^2+(4-1)^2)#
#=sqrt(1^2+3^2)#
#=sqrt(1+9)#
#=sqrt10#
#=3.2#
Therefore Circumference of the Circle #=2pir=2pitimes3.2=19.87#
Arc covers #(13pi)/8# radians on the Circle
In other words Arc covers #(13pi)/8-:2pi=13/16times #(circumference of the Circle)
Therefore Length of the Arc #=13/16 times2pir=13/16 times19.87=16.14#

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