Question

A circle's center is at `(2 ,4 )` and it passes through `(1 ,2 )`. What is the length of an arc covering `(5pi ) /4` radians on the circle?

Answer 1

Length of the Arc `=8.8`

Explanation:

Circle's center is at `(2,4)` and it passes through `(1,2)`
Therefore Length of the `radius=r` =Distance between these points`(2,4) and (1,2)`
or
`radius =r=sqrt((2-1)^2+(4-2)^2)`

`=sqrt(1^2+2^2)`

`=sqrt(1+4)`

`=sqrt5`

`=2.24`

Therefore Circumference of the Circle `=2pir=2pitimes2.4=14.07`
Arc covers `(5pi)/4` radians on the Circle
In other words Arc covers `(5pi)/4-:2pi=5/8times`(circumference of the Circle)
Therefore Length of the Arc `=5/8 times2pir=5/8 times14.07=8.8`