Conic sections
NOTE: When you move the slider "position of the plane" the curve does not change its type. (It is always a circle, an ellipse, etc)
1. When is 40 and is 35 the intersection of the plane and the (double) cone is a hyperbola. Find all the pairs () with this property, (that is, the intersection of the plane and the cone is a hyperbola).
2. For which values of () the intersection of the plane and the cone is an ellipse?
3. For which values () of the intersection of the plane and the cone is a circle?
4. For which values of () the intersection of the plane and the cone is a parabola?
5. Can you find any other curve as the intersection of the plane and the cone?