Question

A circle's center is at `(3 ,2 )` and it passes through `(5 ,8 )`. What is the length of an arc covering `(7pi ) /4` radians on the circle?

Answer 1

Length of the Arc `=34.77`

Explanation:

Circle's center is at `(3,2)` and it passes through `(5,8)`
Therefore Length of the `radius=r` =Distance between these points`(3,2) and (5,8)`
or
`radius =r=sqrt((5-3)^2+(8-2)^2)`
`=sqrt(2^2+6^2)`
`=sqrt(4+36)`
`=sqrt40`
`=6.32`
Therefore Circumference of the Circle `=2pir=2pitimes6.32=39.74`
Arc covers `(7pi)/4` radians on the Circle
In other words Arc covers `(7pi)/4-:2pi=7/8times`(circumference of the Circle)
Therefore Length of the Arc `=7/8 times2pir=7/8 times39.74=34.77`