# A circle's center is at (1 ,5 ) and it passes through (4 ,8 ). What is the length of an arc covering (pi ) /3  radians on the circle?

Jan 31, 2016

$\sqrt{2} \pi$

#### Explanation:

suppose, the equation of the circle is,

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

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

${\left(4 - 1\right)}^{2} + {\left(8 - 5\right)}^{2} = {r}^{2}$

$\mathmr{and} , {r}^{2} = 9 + 9$

$\mathmr{and} , r = 3 \sqrt{2}$

for the length of an arc, we know,

$s = r \theta$

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

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

$= \sqrt{2} \pi$