Question

A circle's center is at `(4 ,2 )` and it passes through `(6 ,2 )`. What is the length of an arc covering `(5pi ) /3` radians on the circle?

Answer 1

The arc length is the fraction of the circle (`theta/2pi`) times the circumference. The radius is needed to find the circumference, so find the radius by finding the distance between the center and `(6,2)`, a point on the circle.

We could use the distance formula, or picture the distance between `(4,2)` and `(6,2)` as 2 units, because the y values of the points are the same.
`r=2`

Let arc length `= s`
`s=(theta/(2pi))(2pir)`
`s=thetar`

`s=(5pi)/3*2`

`s=(10pi)/3 "units"`