A circle's center is at #(4 ,6 )# and it passes through #(3 ,1 )#. What is the length of an arc covering #(pi ) /3 # radians on the circle?
The arc length is
First of all, you need to compute the radius.
If you center is at
#r = sqrt((4-3)^2 + (6-1)^2) = sqrt(1 + 25) = sqrt(26)#
Now, the the length of an arc covering the whole circle would be equivalent to the perimeter of a circle,
In your case, you would like to compute an arc covering
Thus, your arc length is