# 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: y^{2} = 2px

If the focus is in the Y-axis,then the formula is x^{2} = 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: y^{2} = 12x

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