Question

A circle's center is at `(5 ,4 )` and it passes through `(1 ,7 )`. What is the length of an arc covering `(5pi ) /8` radians on the circle?

Answer 1

The arc length is `L=(25pi)/8`

Explanation:

To find the arc length we have to find circle's radius. To calculate it we use the given points. The radius is the distance between given points:

`r=sqrt((5-1)^2+(4-7)^2)=sqrt(4^2+(-3)^2)=sqrt(16+9)=5`

Now we can calculate the arc length:

`L=2pir*alpha/(2pi)=r*alpha=(5pi)/8*5=(25pi)/8`