Conic Sections: The Parabola, e = 1

The general equation of the parabola is given by: y² = 4ax, where a is the distance of the focal point (focus) from the vertex. The locus of the moving point P forms the parabola, which is a type of conic section that occurs when the eccentricity e = 1.

Here, we use the distance formula, to calculate the distance from the point P(x,y) to the focus and from P(x,y) to its perpendicular distance to the directrix, in order derive the general formula for the parabola that has its vertex located at (0,0) and focus located at (a,0) and directrix given by x = -a.

The distances are given by:

PF = √[(x - a)² + y²]
PD = |x + a|

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