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 $\frac{π}{3}$ $(pi ) /3$ radians on the circle?

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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 $\frac{π}{3}$ $(pi ) /3$ radians on the circle?

1 Answer

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Answer 1 · 2016-01-30T00:37:18

$s = \frac{π}{3} \sqrt{13}$ $s = pi/3 sqrt(13)$

Explanation:

using distance equation find the radius:
$\sqrt{{(x_{2} - x_{1})}_{2}^{2} - {(y_{2} - y_{1})}_{2}^{2}}$ $sqrt((x_2-x_1)^2 - (y_2-y_1)^2)$
$\sqrt{4 + 9} = \sqrt{13}$ $sqrt(4+9) = sqrt(13)$
now arclength $s = r θ$ $s = rtheta$
$s = \frac{π}{3} \sqrt{13}$ $s = pi/3 sqrt(13)$

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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 $\frac{π}{3}$ $(pi ) /3$ radians on the circle?

1 Answer

Explanation:

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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 π3(pi ) /3 radians on the circle?

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Explanation:

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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 $\frac{π}{3}$ $(pi ) /3$ radians on the circle?