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All sections are obtained when a plane intersects the cones.

If the plane is parallel to the plane of the circle which generates the cones the section will be a circle.


If the plane is inclined to the above plane at an angle that is less than the angle of inclination of the cone, you will get an ellipse.


When the inclination of the plane equals the inclination of the cone you will get a parabola.


Finally, if the inclination of the plane is greater than the inclination of the cone, you will get a hyperbola.

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Q: How is each conical section obtained from a double cone?
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