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Analytic Geometry Reviewer
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Standard Form of EllipseCase 1: Ellipse with center at (h,k) and the major axis is parallel to the x-axis.
1)()(
2
2
2
2
b
ky
a
hx
Standard Form of EllipseCase 2: Ellipse with center at (h,k) and the major axis is parallel to the y-axis
1)()(
2
2
2
2
b
hx
a
ky
Other important formulae to remember
222 bac Relationship between the
coefficients a, b, and c in an ellipse
Other important formulae to remember
a
bLR
22
Length of each latus
rectum (latera recta,
plural)
Other important formulae to remember
a
ba
a
ce
22
Eccentricity of ellipse
ILLUSTRATIVE EXAMPLE:
Find the equation of the ellipse with
vertex at (4,3), and foci at (-3,3) and
(3,3).
ILLUSTRATIVE EXAMPLE:
Find the equation of the ellipse with
vertex at (5,2), and foci at (-4,2) and
(4,2).
ILLUSTRATIVE EXAMPLE:Find the equation of
the ellipse with endpoints of the minor axis (-1,3) and (-1,-1) and a focus at (1,1)
ILLUSTRATIVE EXAMPLE:Find the equation of the ellipse with foci at (2,3) and (2,-1) and an endpoint of minor axis at (4,1).
ILLUSTRATIVE EXAMPLE:
Find the equation of the ellipse with vertices at (-2,1) and (4,1) with
eccentricity of 2/3.
ILLUSTRATIVE EXAMPLE:Find the equation of the ellipse with center at (-2,2),
vertex at (-2,4) and a focus at (-2,3)
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