The word parabola originated as a combination of 2 Greek words, para, which means besides and bole, which means throw. When any heavy object is thrown in air, its trajectory is a parabola. Hence the name.
The eccentricity of parabola, is . Let be the focus and be the directrix. According to the focus-directrix property,
where is any point on the parabola. Using this condition for locus of a point, we get the standard equation of parabola,
- It is symmetric about axis, and it extends to infinity to the right of axis
- Focal distance =
- Latus rectum =
- Parametric equations : , where is the parameter
- The general equation of parabola is of the form or . It can be converted to the standard form by shift of origin and (sometimes) rotation of axes.
Where can you see the parabolic shape?
I) Shape of satellite dish
II) Automobile Headlights (The dim-dip feature)
III) McDonald’s Arches
IV) Mirror Furnace (capable of producing temperatures up to from rays of the Sun)