Dr Shildneck Fall 2014 The Ellipse An ellipse is a locus of points such that the sum of the distances between two fixed points called the foci is always the same The axis that runs through the longer part of the ellipse is called the major axis The points at the ends of the major axis are ID: 661393
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Slide1
Conic Sections: The Ellipse
Dr. Shildneck
Fall, 2014Slide2The Ellipse
An ellipse is a locus of points such that the sum of the distances between two fixed points (called the foci) is always the same.
The axis that runs through the longer part of the ellipse is called the major axis. The points at the ends of the major axis are called the vertices.
The axis that runs through the shorter part of the ellipse is called the minor axis. The points at the ends of the minor axis are called the co- vertices.Slide3Equation of an Ellipse
(h, k
) = center of the ellipse
a
= horizontal distance from center to ellipse
b = vertical distance from center to ellipsec = distance from center to foci, where c2 = a2 – b2 or c2 = b2 – a2 (always do bigger minus smaller)Slide4
Example 1: Graph and find the coordinates of the center, vertices, co-vertices and foci.
Vertices
Co- Vertices
FociSlide5Writing the Equation of an Ellipse
Determine the center (h, k)Determine the values of
a
and
b
.Given a graphGiven the vertices and co-verticesGiven a vertex/co-vertex and focusPlug the values of h, k, a, and b into the equation.* It is always helpful to sketch a quick picture!Slide6Example 2. Write the equation of an ellipse with a vertex at (6, 0) and a co-vertex at (0, 3).Slide7Example 3. Write the equation of an ellipse centered at the origin with a vertex at (5, 0) and focus at (2, 0).Slide8Example 4. Write the equation of an ellipse centered at (3, 5) with a vertex at (9, 5) and
co-vertex at (3, 7).Slide9Example 5. Write the equation of an ellipse with a vertex at (-2, 2) and a co-vertex at (1, 4).