# How do you write the equation of the line that contains the centers of the circles (x – 2)^2 + (y + 3)^2 = 17 and (x – 5)^2 + y^2 = 32?

Oct 16, 2016

$y = - \frac{3}{7} x - \frac{15}{7}$

#### Explanation:

Both equations are in the form -

x-h)^2+(y-k)^2=a^2

In that case the center of the circle is $\left(h , k\right)$

The center of the circle ${\left(x - 2\right)}^{2} + {\left(y + 3\right)}^{2} = 17$ is $\left(2 , - 3\right)$

The center of the circle ${\left(x + 5\right)}^{2} + {y}^{2} = 32$ is $\left(- 5 , 0\right)$

The equation of the line passing through the point is -

$\left(y - {y}_{1}\right) = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \left(x - {x}_{1}\right)$

$y - \left(- 3\right) = \frac{0 - \left(- 3\right)}{- 5 - \left(- 2\right)} \left(x - 2\right)$

$y + 3 = - \frac{3}{7} \left(x - 2\right)$

$y + 3 = - \frac{3}{7} x + \frac{6}{7}$
$y = - \frac{3}{7} x + \frac{6}{7} - 3$

$y = - \frac{3}{7} x - \frac{15}{7}$