1. What is the parabolic shape used for?
The parabolic reflector takes the light emitted from the focus and throws it out along lines parallel to the axis of the parabola. This makes a strong narrow beam of light, ideal for spotlights, car headlights or searchlights.
2. How are parabolas used in telescopes?
The same principle described above works in reverse for telescopes. The light from the distant stars enters the telescope parallel to the axis of the parabola. When it strikes the parabolic mirror it is reflected on to the focus by the exact mathematical reasoning described above. At the focus a small secondary mirror is placed which directs the light to the eyepiece.
Radio telescopes are made in much the same way, but with a radio receiver at the focus to collect the signal.
3. How are hyperbolas used ?
They are probably used the least often of the conics but have one property that has applications. Any point on a hyperbola has the difference from distances from two fixed points always the same. In World War II this property was used to develop a radar detection system to identify the location of a sound.
