Conic sections
Table of Contents
- Ellipses
- Shape of ellipse
- Construction of ellipses
- Hyperbola
- Shape of hyperbola
- Parabola
- Shape of parabola
- Construction of Parabola
- Optical properties
- Tangent of ellipse and light
- Tangent of hyperbola and light
- Tangent of parabola and light
- Tangent of parabola and light
- Conic section
- Conic section
Shape of ellipse
[b]Steps:[/b][br]1. On a wax paper draw a circle with center O [br]2. Take point A inside the circle. [br]3. Fold the paper so that the point А is on the circumference of the circle O. [br]4. Repeat the step 3 for various positions of A on the circle. [br]5. Which shape can you see?[br][br][b]Geogebra construction:[/b] [br]Folding a paper so that point A is on the circumference means drawing the perpendicular bisector of point A and and a point on the circumference. [br][br]See the construction below. [br][br]What are the focuses?[br]What can you see if point A is near (far from) the circumference? [br]What can you see if Point A is near to point O?
Shape of hyperbola
[b]Steps:[/b][br]1. On a wax paper draw a circle with center O [br]2. Take point A outside the circle. [br]3. Fold the paper so that the point А is on the circumference of the circle O. [br]4. Repeat the step 3 for various positions of A on the circle. [br]5. Which shape can you see?[br][br][b]Geogebra construction:[/b] [br]Folding a paper so that point A is on the circumference means drawing the perpendicular bisector of point A and and a point on the circumference. [br][br]See the construction below. [br][br]Is there any relation of points A and O with focuses?[br]What can you see if point A is near (far from) the circumference?
Shape of parabola
[b]Steps:[/b][br]1. On a wax paper draw a line. [br]2. Take a point A outside the line. [br]3. Fold the paper so that the point А is on the line. [br]4. Repeat the step 3 for various positions of A on the line. [br]5. Which shape can you see?[br][br][b]Geogebra construction:[/b] [br]Folding a paper so that point A is on the line means drawing the perpendicular bisector of point A and and a point on the line. [br][br]See the construction below. [br][br]What is the focus?[br]What can you see if point A is near (far from) the line? [br]What can you see if point A is on the line?