Question

A circle's center is at `(1 ,5 )` and it passes through `(4 ,8 )`. What is the length of an arc covering `(pi ) /3` radians on the circle?

Answer 1

`sqrt2pi`

Explanation:

suppose, the equation of the circle is,

`(x-h)^2+(y-k)^2=r^2`

by putting the values of `h,k,x,y` in the equation, we get,

`(4-1)^2+(8-5)^2=r^2`

`or,r^2=9+9`

`or, r=3sqrt2`

for the length of an arc, we know,

`s=rtheta`

`=3sqrt2*pi/3`

`=cancel(3)sqrt2*pi/(cancel(3))`

`=sqrt2pi`