A circle's center is at #(5 ,4 )# and it passes through #(1 ,7 )#. What is the length of an arc covering #(5pi ) /8 # radians on the circle?

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Answer 1 · 2016-11-25T10:10:14

The arc length is #L=(25pi)/8#

To find the arc length we have to find circle's radius. To calculate it we use the given points. The radius is the distance between given points:

#r=sqrt((5-1)^2+(4-7)^2)=sqrt(4^2+(-3)^2)=sqrt(16+9)=5#

Now we can calculate the arc length:

#L=2pir*alpha/(2pi)=r*alpha=(5pi)/8*5=(25pi)/8#