The Ellipse: centered on the origin and
aligned with either the x- or the y- axis
Use your textbook to fill in the chart.
Terminology
Notation
An ellipse:
The foci:
The major axis:
The minor axis:
a is the standard variable associated
with the major axis.
a=
b is the variable associated
with the minor axis.
b=
The vertices of an ellipse:
The Equation of an Ellipse
Aligned along the x-axis (horizontally)
Aligned along the y-axis (vertically)
Graphing an Ellipse
First find the coordinates of the vertices
to solve for the endpoints of the horizontal
To solve for the endpoints of the vertical axis:
axis:
The Ellipse: centered on the origin and
aligned with either the x- or the y- axis
Terminology Key
Notation
An ellipse: the locus of points such that the
sum of the distances from a point on the
ellipse to the two foci is a constant.
The foci: The two points about which an
ellipse is formed
The major axis: The longer axis
The minor axis: The shorter axis
a is the standard variable associated
with the major axis.
a = ½ (the length of the major axis)
b is the variable associated
with the minor axis.
b = ½ (the length of the minor axis)
The vertices of an ellipse: The points of
intersection with the x- and y- axes.
The Equation of an Ellipse
Aligned along the x-axis (horizontally)
Aligned along the y-axis (vertically)
x2/a2 + y2/b2 = 1
x2/b2 + y2/a2 = 1
Graphing an Ellipse
First find the coordinates of the vertices
to solve for the endpoints of the horizontal
To solve for the endpoints of the vertical axis:
axis:
Set y = 0 and solve the equation
Set x = 0 and solve the equation