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

1 Answer
Somebody N.
Apr 21, 2018

#color(blue)((3pisqrt(5))/4)#

Explanation:

If the centre of the circle has coordinates #(3,2)# and the point #(1,1)# lies on the circumference, then the length of the radius is the distance between these points. This can be found using the distance formula.

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#d=sqrt((3-1)^2+(2-1)^2)=sqrt(5)#

If we rotate the terminal side #(3pi)/4# to form a sector, then the angle subtended by the arc at the centre will also be #(3pi)/4#

Arc length is given by:

#rtheta#

#:.#

#sqrt(5)((3pi)/4)=(3pisqrt(5))/4#

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