Question

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?

Answer 1

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`