Aim of the applet
This applet allows for the representation of conics:
ellipse, hyperbola and parabola.
Input data
Ellipse
- Major radius a
- Minor radius b
Hyperbola
Parabola
In addition, the user can move the point P to calculate the
distances between the focus and any point on the curve.
Analytical definition
- The parameters a, b, c, d, e and f of the ecuation
Output data
Ellipse
- Drawn ellipse with focus represented
- Expression of the ellipse
- Eccentricity of the ellipse
- Evaluation point P
- Distance between focus and the point P
Hyperbola
- Drawn hyperbola with focus represented
- Expression of the hyperbola
- Evaluation point P
- Distance between focus and the point P
Parabola
- Drawn parabola with focus represented
- Expression of the parabola
- Evaluation point P
- Distance between focus and the point P
Analytical definition
- Drawn conic shape.
- Expression of the conic
Firsts steps
- Draw the ellipse of semiaxes a = 6 b = 4. By the mouse, move a and get a circumference.
What happened to the two focus?
How do you flatten the ellipse as possible and what is the value of the eccentricity in this case?
- Build the hyperbola for a = 2 and b = 4.
Slide the blue point on the graph to see the property of the constant difference of distances to the focus.
By the sliders changes the values of a and b to get an ellipse, in which case there is an ellipse?
- Find a parable whose distance between the focus and points is 8.
What are the coordinates of the focus in this case?
- Draw the conic -x2+1.8xy+3y2+4x-2.4y=0. What kind is it?
