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Loci problem

I was asked as below. HELP me pls how to solve.
Suppose u found required loci to be the figures indicated. Describe the different possible sets of points the two loci could have in common.
1. Two lines
3. A line and a plane
3. Two unequal circles in the same plane
4. Two unequal spheres
5. Two parallel lines and a sphere
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Hasufel
16
1) 2 lines might only cross or coincide, so either one point, or an infinite set of points

2) the line might go through the plane, or coincide with it, so....

3) 2 circles may touch or intersect. Think about HOW they would do this. At how many points does one circle touch another?/ at how many points might 2 unequal circles cross eachother?

4) same principle as 3, but now in 3D. Think about 2 Bubbles - one might be touching the other, or they might be stuck together with part of one inside the other. - what shape does the outline of that trace?

5) Visualise this as a football and 2 parallel sticks. The possible loci these could have in common are:

one stick touches the football while the other doesn`t.
both sticks touch the football (the key word is "touch")
one stick touches the football while the other goes right through the football (at how mant points...?)
both sticks go through the football - how many points would this be all together?
both sticks go through the football and are coincidental (one of the parallel lines are the exact same as the other)

(assuming the football stays inflated!)
(edited 10 years ago)

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