Question 1144268: Find an equation of the line containing the centers of the two circles.
X^2+y^2+6x+4y+12=0
X^2+y^2-2x+10y+22=0 Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
The general equation of a circle with center (h,k) and radius r is
In expanded form, that is
Since the problem requires us only to find the centers of the circles, we don't have to do the complete process of completing the square in x and y. We can determine the center (h,k) of each circle from the equations in the given form.
First circle: --> h = -3 --> k = -2
The center of the circle is (-3,-2)
Second circle: --> h = __ --> k = __
I will assume you then know at least one way to find an equation of the line containing those two centers.
To determine the centers, complete the squares for x- and y-terms separately in each equation.
I can do it MENTALLY : for the first circle the center is the point (-3,-2);
for the second circle the center is the point ((1,-5).
To find the equation of the line through the centers, find the slope first
m = = = = = .
Then an equation you are looking for is
= , or
= , or, equivalently,
y + 2 = .(x+3).
From this form, you can transform this equation to any other equivalent form you want.
