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

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Answer 1 · 2016-01-30T00:37:18

$s = pi/3 sqrt(13)$

using distance equation find the radius:
$sqrt((x_2-x_1)^2 - (y_2-y_1)^2)$
$sqrt(4+9) = sqrt(13)$
now arclength $s = rtheta$
$s = pi/3 sqrt(13)$

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