Conic Sections
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 Problem (1)
2. Locus Construction 1
3. Parabola as a Locus
4. Parabola (Graph & Equation Anatomy)
5. Parabola: Geometric Property (I)
6. Parabola: Geometric Property (II)
7. Another Parabola Theorem!
3. Ellipse
1. Locus Problem (2)
2. Locus Construction 2
3. Ellipse (Locus Construction)
4. Ellipse (Graph & Equation Anatomy)
5. Ellipse: Magic Sum = ?
6. Ellipse: Magic Sum = ? (V2)
7. Ellipse: Reflective Property
8. Ellipse: Reflective Property
4. Hyperbola
1. Locus Problem (3)
2. Locus Construction 3
3. Hyperbola (Locus Construction)
4. Hyperbola (Graph & Equation Anatomy)
5. Hyperbola: Difference = ?
6. Hyperbola: Reflective Property
5. Others
1. Locus Constructions (via Paper Folding)

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Conic Sections

Tim Brzezinski, asr5124, Mar 22, 2017

Conic Sections: Circle, Ellipse, Parabola, & Hyperbola Applets

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
Parabola
1. Locus Problem (1)
2. Locus Construction 1
3. Parabola as a Locus
4. Parabola (Graph & Equation Anatomy)
5. Parabola: Geometric Property (I)
6. Parabola: Geometric Property (II)
7. Another Parabola Theorem!
Ellipse
1. Locus Problem (2)
2. Locus Construction 2
3. Ellipse (Locus Construction)
4. Ellipse (Graph & Equation Anatomy)
5. Ellipse: Magic Sum = ?
6. Ellipse: Magic Sum = ? (V2)
7. Ellipse: Reflective Property
8. Ellipse: Reflective Property
Hyperbola
1. Locus Problem (3)
2. Locus Construction 3
3. Hyperbola (Locus Construction)
4. Hyperbola (Graph & Equation Anatomy)
5. Hyperbola: Difference = ?
6. Hyperbola: Reflective Property
Others
1. Locus Constructions (via Paper Folding)

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

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

1.2.

1.3.

1.4.

2.

Parabola

2.1.

Locus Problem (1)

In the applet below, [br][br][i][color=#1e84cc][b]F[/b][/color][/i][color=#1e84cc][b] is a point[/b] [/color]that is not on line [i]d[/i]. [br][b]Point [i]D[/i] is a point that lies ON [color=#666666]the line that passes through [i]A [/i]and [i]B[/i][/color]. [br][/b]The [color=#ff00ff][b]pink line[/b][/color] is the [color=#ff00ff][b]perpendicular bisector[/b][/color] of the segment with endpoints [i][color=#1e84cc][b]F[/b][/color][/i] and [i][b]D[/b][/i]. [br][br]Drag [b]point [i]D[/i][/b] along the line. What do you see? Describe in detail! [br] [br]Feel free to alter the locations of [color=#666666][i][b]A,[/b][/i][/color] [i][color=#666666][b]B[/b][/color], [/i]and/or [i][color=#1e84cc][b]F[/b][/color][/i][color=#666666]. [br][/color]Then [color=#38761d][b]clear the trace[/b][/color] and drag [b]point [i]D[/i][/b] along [color=#666666][b]the line[/b][/color] again. [br][br]Why does this occur?

Please go to the [url=https://www.geogebra.org/m/sduBXC6P]Locus Construction 1 Task[/url] and begin!

2.2.

2.3.

2.4.

2.5.

2.6.

2.7.

3.

Ellipse

3.1.

Locus Problem (2)

In the applet below, [br][br][color=#1e84cc][b][i]O[/i] is the center [/b][/color]of the circle shown. [br][b]Point [i]D[/i] is a point that lies ON this circle. [/b][br][color=#1e84cc][b]Point [i]A[/i] is a point that ALWAYS LIES INSIDE[/b] [/color]the circle. (You can move it anywhere you'd like). [br]The [color=#ff00ff][b]pink line[/b][/color] is the [color=#ff00ff][b]perpendicular bisector[/b][/color] of the segment with endpoints [i]A[/i] and [i]D[/i]. [br][br]Drag [b]point [i]D[/i][/b] around the circle a few times. What do you see? Describe in detail! [br] [br]Feel free to alter the locations of [i][color=#1e84cc][b]A[/b][/color][/i] and [i][color=#1e84cc][b]R[/b][/color]. [/i]Then clear the trace and drag [b]point [i]D[/i][/b] around again. [br][br]Why does this occur?

Please go to the [url=https://www.geogebra.org/m/TZu6tRwE]Locus Construction 2 Task[/url] & begin!

3.2.

3.3.

3.4.

3.5.

3.6.

3.7.

3.8.

4.

Hyperbola

4.1.

Locus Problem (3)

In the applet below, [br][br][color=#1e84cc][b][i]O[/i] is the center [/b][/color]of the circle shown. [br][b]Point [i]D[/i] is a point that lies ON this circle. [br][/b][color=#1e84cc][b]Point [i]A[/i] is a point that ALWAYS LIES OUTSIDE[/b] [/color]the circle. (You can move it anywhere you'd like). [br]The [color=#ff00ff][b]pink line[/b][/color] is the [color=#ff00ff][b]perpendicular bisector[/b][/color] of the segment with endpoints [i]A[/i] and [i]D[/i]. [br][br]Drag [b]point [i]D[/i][/b] around the circle a few times. What do you see? Describe in detail! [br] [br]Feel free to alter the locations of [i][color=#1e84cc][b]A[/b][/color][/i] and [b]the gray point (radius changer)[/b][i]. [br][/i]Then clear the trace and drag [b]point [i]D[/i][/b] around again. [br][br]Why does this occur?