How many points of intersection can occur between two identical shapes?

[yorrichany]

I have a question based on two math questions that I saw.
The first one says- the ellipse shown below intersects any different ellipse in, at most how many points.
The second one says- the figure below is a pentagon (5-sided figure). Suppose a second pentagon were overlaid on this pentagon. At most, the two figures could have how many points of intersection?
Both of the images that came with the questions were very generic photos of an ellipse and a pentagon. My question is why the answer to the first question was 4 while the answer to the second was infinitely many. I thought that the answer to the first one should be infinitely many as well. These questions both came from an ACT practice test if anyone is wondering.

 

[JeffM]

I must say I find these rather silly problems based on what you have said. It is REALLY important to tell us what the problem says EXACTLY AND COMPLETELY. The first one probably uses the words "different" ellipse; therefore it cannot coincide in every point; if it did, it would be identical. The second one probably says something like "another" pentagon, which, if the two pentagons had sides of identical length and an identical sequence of angles of equal measure, could be made to coincide everywhere. If that is the case, it seems to be a problem in reading comprehension instead of math.

I admit that careful definition of problems is part of being able to use math, but close semantic parsing of texts is not.

EDIT: Being able to do math, however, may contribute to the capacity for close semantic parsing. I had an acquaintance who was first a math major and then a law student at Harvard, and he and I once analyzed a regulation using symbolic logic. Needless to say, anyone who does that sort of thing too often will come to a bad end. Take it easy on mixing math and semantics. Once and a while may not hurt, but over-indulgence is deleterious.

 

[yorrichany]

thanks for you reply, I found these questions to be quite weird as well. I copy and pasted them exactly how they appeared on the ACT practice book.