Question

A circle has a center at `(3 ,0 )` and passes through `(0 ,1 )`. What is the length of an arc covering `(3pi ) /4` radians on the circle?

Answer 1

`s ~~ 7.451`

Explanation:

Arc length is computed using the formula `s = r * theta`

The center of the circle is on `(3, 0)` and it passes through `(0, 1 )`. Given these two points, we can determine the radius of the circle since we know that the radius is the distance from the center to any point on the circle.

[Solving for Radius]
Using the distance formula: `sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)`

`d = sqrt((0-3)^2 + (1 - 0)^2)`
`d = sqrt((-3)^2 + (1)^2)`
`d = sqrt(9 + 1)`
`d = sqrt(10)`

Using the arc length formula...

`s = sqrt10 * (3pi)/4`
`s ~~ 7.451`