Intersection of 2 circles

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Skelly4444

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Apr 4, 2019
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We have 2 circles C1 and C2 and need to find the coordinates of intersection.

C1 has its centre at (-2 , 5) and radius 7cm
C2 has its centre at (12 , 5 and radius 16cm

Drawing this out yields the approximate coordinates of (-2.39 , -2) and (-2.39 , 12)

However when I solve the equations algebraically, I can get the x coordinate of -2.39 easily but when I plug it back into one of the circle equation to solve for y, I end up with y values of 11.99 and -0.29. The first one is obviously correct but I cannot seem to obtain the other y value no matter what I do. The quadratic formula is kicking out a spurious value that isn't right?

How can I obtain the other value without drawing it to scale on a piece of paper?
 
Skelly4444 said:
We have 2 circles C1 and C2 and need to find the coordinates of intersection.

C1 has its centre at (-2 , 5) and radius 7cm
C2 has its centre at (12 , 5 and radius 16cm

Drawing this out yields the approximate coordinates of (-2.39 , -2) and (-2.39 , 12)

However when I solve the equations algebraically, I can get the x coordinate of -2.39 easily but when I plug it back into one of the circle equation to solve for y, I end up with y values of 11.99 and -0.29. The first one is obviously correct but I cannot seem to obtain the other y value no matter what I do. The quadratic formula is kicking out a spurious value that isn't right?

How can I obtain the other value without drawing it to scale on a piece of paper?
Click to expand...
Please show your work, so we can see what went wrong.

It may just be an arithmetic error, or an order of operations error.
 
Thank you for your response, I managed to find a mathematical error in my working, a basic sign error in the end.
 
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