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Ellipse Properties and Equation Derivation: A High School Math Exercise, Study notes of Mathematics

Mathematics

A comprehensive set of exercises for high school students to practice their understanding of ellipses. It covers key concepts like center, vertices, co-vertices, foci, major and minor axes, domain, and range. The exercises also involve deriving the equation of an ellipse given specific parameters and calculating eccentricity. Ideal for reinforcing foundational knowledge in conic sections and preparing students for more advanced mathematical concepts.

Typology: Study notes

2024/2025

Uploaded on 03/21/2025

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Ellipses
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Ellipses

Parts of an ellipse

Determine the following elements and make it’s graph

Center, Vertices, Co-Vertices, Foci, Mayor Axis, Minor Axis, Domain & Range

Determine the following elements and make it’s graph

Center, Vertices, Co-Vertices, Foci, Mayor Axis, Minor Axis, Domain & Range

Center (-1,4) a = 8 b = 6

Center (-1,4) a = 8 b = 6

Co-Vertices, b distance away from the center

Foci, c distance away from the center

Determine the following elements and make it’s graph

Center, Vertices, Co-Vertices, Foci, Mayor Axis, Minor Axis, Domain & Range

Mayor axis = 2a = 16 Minor axis = 2b = 12

Domain =[-7,5] Range =[-4,12]

Find the equation for an ellipse with center at (3,-1) minor axis of 6 and one vertex at (-2,-1)

Eccentricity

The eccentricity of an ellipse measures how flat or round an ellipse is. The eccentricity value of all ellipses is always less than one. Eccentricity as 1 is a straight line, and zero will be a perfect circle.

distance from the center to a focus distance from the center to a vertex

e=

Exercise

Find the eccentricity for

Exercise

Find the eccentricity for

Exercise

Find the eccentricity for

Exercise

Find the eccentricity for