parabola

The parabola is the geometric place of all points in a plane that are equidistant to a fixed point, called focus, and a fixed straight line, called directrix.
d(P,F) = d(P,d) = p/2

Its formula is: y² = 2px

If the focus is in the Y-axis,then the formula is x² = 2py.

The eccentricity is always 1, e = 1.

You can see parabolas:
- In parabolic antennas, because of the property of the parabolas: any wave that comes parallel to the parabola axis, is reflected to the focus.

- In Architecture, the parabolic cables are used for the suspension of some bridges (for example the Golden Gate), because the load applied in the horizontal direction produces a uniform strain in the cable.

Exercise: Calculate the locus of the points that are equidistant to the point (3,0) and the straight line x + 3 = 0

Solutions: y² = 12x