A circle's center is at #(4 ,0 )# and it passes through #(6 ,9 )#. What is the length of an arc covering #(5pi ) /3 # radians on the circle?

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Answer 1 · 2016-09-29T18:49:58

#s = sqrt(85)*(5pi)/3 ~~ 48.27#

First we must find the radius of the circle.

We know the distance from the center to any point it passes through is the radius.

So, using the distance formula: #d = sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#d = sqrt((4-6)^2+(0-9)^2) = sqrt(85)#

So, the radius is #sqrt(85)#

And we know the formula for arc length is: #s = rtheta#
Where s is the arc length, r is the radius, and theta is the angle in radians.

Plugging in, #s = sqrt(85)*(5pi)/3#

Answer 2 · 2016-09-29T18:51:16

#s = 5sqrt(85)pi/3#

Let r = the radius

#r = sqrt((6 - 4)^2 + (9 - 0)^2)#

#r = sqrt(85)#

Let s = the arc length

#s = rtheta# where #theta# is the given angle

#s = 5sqrt(85)pi/3#