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

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Answer 1 · 2016-02-03T10:49:22

$sqrt2/3pi$

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

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

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

$or,1+4=r^2$

$or,r=sqrt5$

again, we know,

$s=rtheta$

$=sqrt2*pi/3$

$=sqrt2/3pi$

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 (pi ) /3 (pi ) /3 radians on the circle?