Question

A circle's center is at `(3 ,9 )` and it passes through `(4 ,5 )`. What is the length of an arc covering `( pi ) /6` radians on the circle?

Answer 1

Arc Length: `s=R.\theta=\frac{\pi}{6}.\sqrt(17)` units

Explanation:

The distance between points (`x_0, y_0`) and (`x,y`) is :
`\sqrt((x-x_0)^2+(y-y_0)^2)`

Radius is the distance between the centre (`x_0, y_0`) and a point on the circle (`x,y`).

Radius: `R=\sqrt((4-3)^2+(5-9)^2)=\sqrt(17)` units,
Arc Length: `s=R.\theta=\frac{\pi}{6}.\sqrt(17)` units