one student identifies four types of conic sections. another says there are only three types(hyperbole, circle, and ellipse), who is correct? explain how conic sections are found
Both students are correct in a way. There are technically four types of conic sections: the circle, ellipse, parabola, and hyperbola. However, the first student may not have mentioned the parabola when listing the types.
Conic sections are found by intersecting a plane with a cone. Depending on the angle of intersection and the position of the plane, different shapes are formed.
- A circle is formed when the plane intersects the cone at a right angle.
- An ellipse is formed when the plane intersects the cone at an angle that is less than the angle of the cone.
- A parabola is formed when the plane intersects the cone parallel to one of the sides of the cone.
- A hyperbola is formed when the plane intersects the cone at an angle greater than the angle of the cone.
So, in summary, there are indeed four types of conic sections, and the first student is correct in stating this.