Conic Sections- Maths Made Easy

Tim Brzezinski, Maths Made Easy Suresh, Feb 26, 2020

Conic Sections: Circle, Ellipse, Parabola, & Hyperbola Applets Grade 11 NCERT CBSE Conic section

Table of Contents

  1. Circles
    1. Circle Equation: Center (0,0)
    2. Circle Equation: Center NOT (0,0)
    3. Circle Equation: Center (h,k)
    4. Equation & Graph of a Circle
  2. Parabola
    1. Locus Construction 1
    2. Parabola as a Locus
    3. Parabola (Graph & Equation Anatomy)
    4. Parabola: Geometric Property (II)
  3. Ellipse
    1. Locus Construction 2
    2. Ellipse: Reflective Property
    3. Ellipse: Reflective Property
    4. Ellipse (Locus Construction)
    5. Ellipse (Graph & Equation Anatomy)
  4. Hyperbola
    1. Locus Construction 3
    2. Hyperbola (Locus Construction)
    3. Hyperbola (Graph & Equation Anatomy)
    4. Hyperbola: Difference = ?
  5. Others
    1. Locus Constructions (via Paper Folding)

1.

Circles

  • 1. Circle Equation: Center (0,0)
  • 2. Circle Equation: Center NOT (0,0)
  • 3. Circle Equation: Center (h,k)
  • 4. Equation & Graph of a Circle

1.1.

Circle Equation: Center (0,0)

For the questions below, be sure to zoom out if you need to!
1.
Suppose [i]P(x,y)[/i] = any point that lies on a circle with center (0,0) and radius 5. [br]Use what you've observed to write an equation that expresses the relationship among [i]x[/i], [i]y[/i], and [i]r[/i].
2.
What is the equation of a circle with center (0,0) and radius [i]r[/i] = 9?
3.
Suppose another circle has center (0,0). Suppose this circle also passes through the point (12, -5).[br]Write the equation of this circle. [br]
4. FINAL QUESTION:
Suppose [i]P(x,y)[/i] = any point that lies on a circle with center (0,0) and radius [i]r[/i], where [i]r[/i] > 0. [br]Use what you've observed to write an equation that expresses the relationship among [i]x[/i], [i]y[/i], and [i]r[/i].
Quick (Silent) Demo
– Tim Brzezinski

1.2.

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1.3.

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1.4.

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2.

Parabola

  • 1. Locus Construction 1
  • 2. Parabola as a Locus
  • 3. Parabola (Graph & Equation Anatomy)
  • 4. Parabola: Geometric Property (II)

2.1.

Locus Construction 1

Locus Construction 1 Lesson Activity
– Tim Brzezinski

2.2.

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2.3.

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2.4.

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3.

Ellipse

  • 1. Locus Construction 2
  • 2. Ellipse: Reflective Property
  • 3. Ellipse: Reflective Property
  • 4. Ellipse (Locus Construction)
  • 5. Ellipse (Graph & Equation Anatomy)

3.1.

Locus Construction 2

Locus Construction 2: Lesson Activity
Quick Demo. (BGM: Andy Hunter)
– Tim Brzezinski

3.2.

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3.3.

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3.4.

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3.5.

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4.

Hyperbola

  • 1. Locus Construction 3
  • 2. Hyperbola (Locus Construction)
  • 3. Hyperbola (Graph & Equation Anatomy)
  • 4. Hyperbola: Difference = ?

4.1.

Locus Construction 3

Locus Construction 3: Lesson Activity
– Tim Brzezinski

4.2.

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4.3.

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4.4.

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5.

Others

  • 1. Locus Constructions (via Paper Folding)

5.1.

Locus Constructions (via Paper Folding)

Locus Construction (I)
[url=https://www.geogebra.org/m/sduBXC6P]Locus Construction (I)[/url] - [color=#0000ff]with GeoGebra[/color]
Locus Construction (II)
[url=https://www.geogebra.org/m/TZu6tRwE]Locus Construction (II)[/url] - [color=#0000ff]with GeoGebra[/color]
Locus Construction (III)
[url=https://www.geogebra.org/m/yXDC8N93]Locus Construction (III)[/url] - [color=#0000ff]with GeoGebra[/color]
– Tim Brzezinski

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