Is it the line connecting the 2 points of intersection between the circles?
Hi, I am struggling with this problem . I do not know the properties of circles so well, so I gave the variables some values and drew, but I still don't get anything :-/. It would also be great if you could tell me how you know (what rule, etc.) you have used to answer the question. Thanks!
The problem says:
Let , be two intersecting circles. Deviding the first equation by a and the second by b and subtracting, we obtain the equation of a line:
What is this line?
For starters, the intersection is 0 points, 1 point, 2 points, or infinitely many points in a circular locus. If you are doing something that leads to a linear equation, that seems kind of magic, doesn't it? Why would you believe that would work? It might. Feel free to prove it. Note: It does give the equation of the line, but it does NOT give the points of intersection.
Second, not everything that looks like that is a circle. There must be relationships between the parameters. If you enforce the relationships, you will see that it is all quite a bit simpler. Expand , and put it in that standard form. You will see the necessary relationships.
Have you a particular numerical example that you find vexing?
Exploration: If there is no intersection, what does it produce? It's a line perpendicular to what?