Question

A circle's center is at `(2 ,4 )` and it passes through `(1 ,3 )`. What is the length of an arc covering `( pi ) /3` radians on the circle?

Answer 1

≈ 1.481

Explanation:

To calculate length of arc , require to know radius of circle. This can be found using the centre and point on circle.
Using the `color(blue)" distance formula "`

`d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)`

where`(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate pints "`

let `(x_1,y_1)=(2,4)" and " (x_2,y_2)=(1,3)`

so radius (r) =d `= sqrt((1-2)^2 + (3-4)^2) = sqrt2`

length of arc = `2pir xx " fraction covered "`

`= 2pixxsqrt2 xx (pi/3)/(2pi) = sqrt2 xxpi/3 ≈ 1.481`