A circle's center is at $(1, 5)$ $(1 ,5 )$ and it passes through $(2, 3)$ $(2 ,3 )$ . What is the length of an arc covering $\frac{π}{3}$ $(pi ) /3$ radians on the circle?

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Answer 1 · 2016-02-03T10:49:22

$\frac{\sqrt{2}}{3} π$ $sqrt2/3pi$

suppose,
the equation of the circle is,
${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ $(x-h)^2+(y-k)^2=r^2$

by putting the value of $x, y, h, k$ $x,y,h,k$ in the equation, we get,

${(2 - 1)}^{2} + {(3 - 5)}^{2} = r^{2}$ $(2-1)^2+(3-5)^2=r^2$

$or, 1 + 4 = r^{2}$ $or,1+4=r^2$

$or, r = \sqrt{5}$ $or,r=sqrt5$

again, we know,

$s = r θ$ $s=rtheta$

$= \sqrt{2} \cdot \frac{π}{3}$ $=sqrt2*pi/3$

$= \frac{\sqrt{2}}{3} π$ $=sqrt2/3pi$

A circle's center is at (1 ,5 )(1,5)(1 ,5 ) and it passes through (2 ,3 )(2,3)(2 ,3 ). What is the length of an arc covering (pi ) /3 π3(pi ) /3 radians on the circle?