Aim #55-56: How do we analyze the graph of an ellipse?
HW Packet Due Friday 2/10
Quiz (Aims 55-58) Monday 2/13 AND
Test (Aims 52-58) Wednesday 2/15
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2
Do Now: Sketch the graph of x + y = 1
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1
Aim #55-56: How do we analyze the graph of an ellipse?
HW Packet Due Friday 2/10
Quiz (Aims 55-58) Monday 2/13 AND
Test (Aims 52-58) Wednesday 2/15
Do Now: Determine the center, and the lengths of the
major and minor axes:
Ellipse
An ellipse is the set of all points P in the plane the sum of whose
distances from two fixed points, called the foci, is a constant.
Major Axis: longer axis containing the foci
Center: the midpoint of the foci
Minor Axis: line through t he center
perpendicular to the major axis
The vertices are the points of intersection between the ellipse and
major axis.
a = center to vertices (always largest) b = center to "minor pts"
c = center to foci
Ellipses are, by their nature, not "perfectly round" in the technical
sense that circles are round. The measure of the amount by which an
ellipse is "squished" away from being perfectly round is called the
ellipse's eccentricity, and the value of an ellipse's eccentricity is
denoted as e = c/a.
Recall:
c
e = __
a
c = distance from center to
either focus point
a = distance from center to
either vertex on major axis
In an ellipse, the following is always true: b2 + c2 = a2
Find the center, vertices, foci, and major/minor axis.
Also determine the ellipses eccentricity.
Find the center, vertices, foci, and major/minor axis.
Also determine the ellipses eccentricity.
center ( , ) major ­axis a= vertices minor ­axis b= minor pts
Find an equation of the ellipse with center at the origin, one focus
at (3,0), and a vertex at (-4, 0). Graph the equation.
Find an equation for the ellipse with center at (2, -3), one focus at
(3, -3) and one vertex at (5, -3). Graph the ellipse.
Find the center, vertices, foci, and major/minor axis.
Also determine the ellipses eccentricity.
Find the center, vertices, foci, and major/minor axis.
Also determine the ellipses eccentricity.
Find an equation of the ellipse having one focus at (0, 2) and
vertices at (0, -3) and (0, 3). Graph the ellipse.
Find the equation for an ellipse with vertices at (8,3) and (-4,3)
and one focus at (6,3).
MIXED PRACTICE:
A) For each equation below, find the center, vertices, foci, and
major/minor axis. Determine the ellipse's eccentricity and sketch a
graph.
B) Find the equation for an ellipse with vertices at (8,3) and
(-4,3) and one focus at (6,3).
Attachments
ellipse.gsp
Ellipse and foci resised.gsp