Conic sections and interpntration of solids

Consider a right circular cone, i.e. a cone whose base is a circle and whose apex is above the centre of the base (Fig. 12.1). The true face of a section through the apex of the cone will be a triangle.

Conic Perspective Drawing
Fig. 12.1 Conic sections: section AA - triangle; section BB - circle; section CC - parabola; section DD - hyperbola; section EE - rectangular hyperbola; section FF - ellipse

The true face of a section drawn parallel to the base will be a circle.

The true face of any other section which passes through two opposite generators will be an ellipse.

The true face of a section drawn parallel to the generator will be a parabola.

If a plane cuts the cone through the generator and the base on the same side of the cone axis, then a view on the true face of the section will be a hyperbola. The special case of a section at right-angles to the base gives a rectangular hyperbola.

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