A circle has a center at $(7, 9)$ $(7 ,9 )$ and passes through $(1, 3)$ $(1 ,3 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?

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A circle has a center at $(7, 9)$ $(7 ,9 )$ and passes through $(1, 3)$ $(1 ,3 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?

1 Answer

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Answer 1 · 2016-01-24T18:41:06

Use the circle standard form

Explanation:

Circle equation standard form:
${(x - 7)}^{2} + {(y - 9)}^{2} = 61$ $(x-7)^2 + (y-9)^2 = 61$
circle centered at (7, 9)
Circumference, $C = D π; D = 2 r$ $C = Dpi; D = 2r$
Thus arc length of the $\frac{3}{4} π$ $3/4pi$
$a_{\frac{3}{4} π} = \frac{3}{4} π D = \frac{3}{2} \sqrt{61}$ $a_(3/4pi)= 3/4pi D = 3/2 sqrt(61)$

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A circle has a center at $(7, 9)$ $(7 ,9 )$ and passes through $(1, 3)$ $(1 ,3 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?

1 Answer

Explanation:

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A circle has a center at $(7, 9)$ $(7 ,9 )$ and passes through $(1, 3)$ $(1 ,3 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?