Conic Sections – the Ellipse, the Parabola, the Hyperbola

Figure 11.1 shows the five sections that can be obtained from a cone. The triangle and the circle have been discussed in earlier chapters; this chapter looks at the remaining three sections: the ellipse, the parabola and the hyperbola. These are three very important curves. The ellipse can vary in shape from almost a circle to almost a straight line and is often used in designs because of its pleasing shape. The parabola can be seen in the shape of electric fire reflectors, radar dishes and the main cable of suspension bridges. Both the parabola and the hyperbola are much used in civil engineering. The immense strength of structures that are parabolic or hyperbolic in shape has led to their use in structures made of pre-cast concrete and where large unsupported ceilings are needed.