well, I have forgotten how to identify ellipse, hyperbola,circle straightline from the general equation of conic, so is there any other way to identify these homeomorphic or not? a) B is an ellipse, b) B is an hyperbola, c) B is an complement of a closed ellipse. please help.
A is a circumference in a. and b. while a disk in c. so...
a. Yes, homeomorphism by isometric transformation to overlay the centers, and then by projection of one onto the other.
b. No, the circumference is compact, while the hyperbola is not
c. No, same reason as b