Geogebra :HSS Mathematics

Visualization of Parabola, Ellipse and Hyperbola In Geogebra

Applications --> Education --> Geogebra

View --> 3D Graphics 

 

 

 

Hide the axes and plane in the 3D graphics. For this Right click on the 3D graphic window and uncheck Axes and Plane.

Make 3 sliders in the Graphics window.

1. Number slider : Name : a

Minimum =-10 Maximum = 10   Increment : 0.01

2. Angle slider : Name α (alpha)

Minimum =10^o   Maximum = 60^o    Increment : 5^o

3. Angle slider : Name β

Minimum =0^o    Maximum = 90^o    Increment : 5^o

Mark three points

1. A=(0,0,0)

2. B=(0,0,1)

3. C= (0,0,a) Where a is the variable ( name of the number slider). By moving the slider we can see a point is moving along the x axis.

Draw three lines

1. f = Line through C and (1,0,a) . For this use the command Line[C,(1,0,a)] in the input bar.

2. g = Line through (0,0,0) and (0,sin(β),cos(β)) . For this use the command

Line[(0,0,0) (0,sin(β),cos(β))] in the input bar.

3. h = Line through C parallel to line g. For this use the command

Line[C,g] in the input bar.

Draw a vector AB. For this use the command Vector[A,B] (here its name is u. We can see this from the algebraic view)

Vector[ <Start Point>, <End Point> ]

For drawing conic use the command Cone[A,u,α] in the input bar. (Here its name is b)

Cone[ <Point>, <Vector>, <Angle>].

Hide all the three lines .

 

Draw a plane through the lines f and h . For this use the command Plane[f,h] in the input bar. From the algebraic view we can understand the name of the plane. Here it is c.

Now we can mark the intersection between the conic and the plane by using the command IntersectPath[b,c]

IntersectPath[ <Plane>, <Quadric> ]

Include texts Parabola, Ellipse and Hyperbola in the 3d Graphics.

 

Use Check boxes to show or hide the plane and cone.

Download Geogebra applet