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Summary PRE CALCULUS - Ellipse
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  • Pre-Calculus
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Summary notes on the topic discussions on the definition, properties, illustration, graphs, and computation about the Ellipse. Includes sample problem and graph illustration with a suggested answers. An assessment of learning about the topic is also provided with an answer.

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Document information

  • June 19, 2023
  • 13
  • 2022/2023
  • Summary

Subjects

  • shs
  • senior high school
  • grade 11
  • stem
  • stem 11
  • shs 11
  • mathematics
  • math 11
  • conic section
  • graph
  • calculus
  • pre calculus

Written for

  • Secondary school
  • Pre-Calculus
  • 4
All documents for this subject (21)

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rustylouierombawa

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, I. Objectives

At the end of the discussion, the learners will be able to:

1. Define the ellipse.
2. Transform general form of equation to the standard form equation of an ellipse and vice
versa.
3. Find the foci, vertices and co-vertices given the equation of the ellipse at the center of
(0,0) or (h,k).
4. Identify if it is in horizontal or vertical form.
5. Graph the standard form equation of ellipse.

II. Discussion

What is ellipse?

Ellipse is formed when the tilted plane intersects only to one cone to form a bounded
curve or an oval shape.

General form

Ax² + By² + Cx + Dy + E = 0

Standard Form

Vertex form of the equation of an ellipse

Center Major axis Equation Graph
(0,0) Horizontal 𝑥² 𝑦²
+ =1
𝑎² 𝑏²




(0,0) Vertical 𝑥² 𝑦²
+ =1
𝑏² 𝑎²




(h, k) Horizontal (𝑥−ℎ)² (𝑦−𝑘)²
+ =1
𝑎² 𝑏²

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