# 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?

Feb 3, 2016

$\frac{\sqrt{2}}{3} \pi$

#### Explanation:

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

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

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

$\mathmr{and} , 1 + 4 = {r}^{2}$

$\mathmr{and} , r = \sqrt{5}$

again, we know,

$s = r \theta$

$= \sqrt{2} \cdot \frac{\pi}{3}$

$= \frac{\sqrt{2}}{3} \pi$