Chapter 8.5, Problem 2E

Solution

To explain : The comparison between the definitions of ellipse and hyperbola.

Ellipse and hyperbola are different from each other.

Given information :

Ellipse and hyperbola.

Explanation :

An ellipse is the set of all points $P$ in a plane such that sum of distances between $P$ and two fixed points called the foci is a constant whereas a hyperbola is the set of all points $P$ in a plane such that difference of distances between $P$ and two fixed points called foci is a constant.

In ellipse, the line through foci that intersects the two vertices is called major axis whereas in hyperbola, the line that intersects the two vertices is called transverse axes.

In ellipse, the line perpendicular to the major axis at the center intersects at two co-vertices is called minor axis whereas a hyperbola has two branches and two asymptotes that contains the diagonals of a rectangle centered at the center of the hyperbola.