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