Question

A circle's center is at `(3 ,1 )` and it passes through `(0 ,2 )`. What is the length of an arc covering `( pi ) /6` radians on the circle?

Answer 1

`(pisqrt10)/6units`

Explanation:

the arc length of is calculated using `color(blue)(s=rtheta)`

where `r` is the radius of the circle

& `theta` is the angle subtended by the arc at the centre of the circle.

1) Find the radius of the circle, this is done by Pythagoras

`r=sqrt((3-0)^2+(1-2)^2`

`r=sqrt(9+1)=sqrt10`

2) arc length

`s=rtheta=sqrt10xxpi/6`

`:.s=(pisqrt10)/6 units`