Question

A circle's center is at `(1 ,5 )` and it passes through `(2 ,3 )`. What is the length of an arc covering `(pi ) /3` radians on the circle?

Answer 1

`sqrt2/3pi`

Explanation:

suppose,
the equation of the circle is,
`(x-h)^2+(y-k)^2=r^2`

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

`(2-1)^2+(3-5)^2=r^2`

`or,1+4=r^2`

`or,r=sqrt5`

again, we know,

`s=rtheta`

`=sqrt2*pi/3`

`=sqrt2/3pi`