SOLUTION: Find an equation of the line containing the centers of the two circles whose equations are given below. (x-6)^2+(y-3)^2=49 (x+4)^2+(y-4)^2=81

Algebra ->  Coordinate-system -> SOLUTION: Find an equation of the line containing the centers of the two circles whose equations are given below. (x-6)^2+(y-3)^2=49 (x+4)^2+(y-4)^2=81      Log On


   



Question 1202856: Find an equation of the line containing the centers of the two circles whose equations are given below. (x-6)^2+(y-3)^2=49 (x+4)^2+(y-4)^2=81
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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line containing the centers of the two circles whose equations are given below. (x-6)^2+(y-3)^2=49 (x+4)^2+(y-4)^2=81
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Say better this way:
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line containing the centers of the two circles whose equations are given below. (x-6)^2+(y-3)^2=49, AND (x+4)^2+(y-4)^2=81
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The two points are (6, 3) and (-4, 4).
IF you already know how to find equation of a line through two given points, then you're all set knowing what to do.

Do you understand why this is or can be used? y-3=-%281%2F10%29%28x-6%29


In more detail,
Picking the point (6, 3) as build the variable slope expression
and both points for the slope value
%28y-3%29%2F%28x-6%29=%284-3%29%2F%28-4-6%29
%28y-3%29%2F%28x-6%29=1%2F%28-10%29
%28y-3%29%2F%28x-6%29=-1%2F10
y-3=-%281%2F10%29%28x-6%29
y-3=-x%2F10%2B6%2F10
y=-x%2F10%2B3%2F5%2B3
highlight%28y=-x%2F10%2B3%263%2F5%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Directly from the equations in the given form of the two circles, the centers are (6,3) and (-4,4).

The "run" from the first center to the second is -10 (from 6 to -4); the "rise" is 1 (from 3 to 4), so the slope (rise over run) is -1/10 = -0.1.

Use that slope in the general slope-intercept form of the equation using either of the two given points to find the equation.

y=mx%2Bb
3=%28-0.1%29%286%29%2Bb
3=-0.6%2Bb
b=3.6

ANSWER: y=-0.1x%2B3.6