A circle's center is at #(3 ,1 )# and it passes through #(4 ,2 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?

1 Answer
Roella W.
Feb 4, 2016

#(pisqrt(2))/6#

Explanation:

The circle equation is #(x-h)^2 +(y-k)^2 = r^2# where #(h,k)# is the centre and #r# is the radius. We can find #r# by substituting in the coordinates of the given point.

#(4-3)^2 +(2-1)^2 = r^2#

#1^2 +1^2 = r^2#

#:. r= sqrt(2)#

The complete circle subtends an angle of #2pi (360^o)# so the arc subtending #pi/6# represents #(pi/6)/(2pi)# of the circumference which is #1/12#

Arc length # = 1/12*(2pir) = 2pisqrt(2)/12 =(pisqrt(2))/6#

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