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• A parabola is the locus of points equidistant from fixed line l and fixed point F
not on the line. Fixed point F is the “focus,” fixed line l is the “directrix,” the
horizontal line that passes through the focus directrix is the “axis of symmetry,”
the length of a straight line that intersects the parabola, passes through the
locus, and is parallel to fixed line l is the “latus rectum,” and point A where the
parabola intersects the axis of symmetry is the “vertex.”
• An ellipse is the locus of points the sum of the distances of each of which from
two fixed points F and F’ is constant. Points F and F’ are the “foci,” points A, A’,
B, and B’ where the ellipse intersects the x- and y-axes are the “vertexes,” the
x-coordinate values of vertexes A and A’ are called x-intercepts, and the y-
coordinate values of vertexes B and B’ are called y-intercepts.
• A hyperbola is the locus of points related to two given points F and F’ such that
the difference in distances of each point from the two given points is constant.
Points F and F’ are the “foci,” points A and A’ where the hyperbola intersects
the x-axis are the “vertexes,” the x-coordinate values of vertexes A and A’ are
called x-intercepts, the y-coordinate values of vertexes A and A’ are called y-
intercepts, and straight lines i and i' , which get closer to the hyperbola as they
move away from the foci are “asymptotes.”
Axis of symmetry
Latus rectum
Directrix
l
Vertex A
Focus F (p, 0)
Graphing an Implicit Function 14 - 2
x
-intercept A’
Focus F’ Focus F
x
-intercept A
y
-intercept B’
y
-intercept B
Focus F' Focus F
Vertex
A’
Vertex
A
Asymptote
l
Asymptote
l'
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