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?

1 Answer
radee
Feb 4, 2016

#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#

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