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

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Answer 1 · 2016-10-16T03:37:52

$y=-3/7x-15/7$

Both equations are in the form -

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

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

The center of the circle $(x-2)^2+(y+3)^2=17$ is $(2,-3)$

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

The equation of the line passing through the point is -

$(y-y_1)=(y_2-y_1)/(x_2-x_1)(x-x_1)$

$y-(-3)=(0-(-3))/(-5-(-2))(x-2)$

$y+3=-3/7(x-2)$

$y+3=-3/7x+6/7$
$y=-3/7x+6/7-3$

$y=-3/7x-15/7$

Refer the diagram also

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