Unformatted text preview: s the set of all points (x, y ) in the plane such that the sum of the distance from F1 to
(x, y ) and the distance from F2 to (x, y ) is d. The points F1 and F2 are called the focia of the
a the plural of ‘focus’ (x, y )
F2 d1 + d2 = d for all (x, y ) on the ellipse We may imagine taking a length of string and anchoring it to two points on a piece of paper. The
curve traced out by taking a pencil and moving it so the string is always taut is an ellipse.
The center of the ellipse is the midpoint of the line segment connecting the two foci. The major
axis of the ellipse is the line segment connecting two opposite ends of the ellipse which also contains
the center and foci. The minor axis of the ellipse is the line segment connecting two opposite
ends of the ellipse which contains the center but is perpendicular to the major axis. The vertices
of an ellipse are the points of the ellipse which lie on the major axis. Notice that the center is also
the midpoint of the major axis, hence it is the midpoint of the vertices. I...
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