What is the directrix of a parabola?

1 Answer
A. S. Adikesavan
May 10, 2016

The locus of the point that is equidistant from a point and a straight line is called a parabola. The point is called the focus of the parabola and the straight line is called the directrix.

Explanation:

If (x, y) is a point on a parabola having #(alpha, beta)# as focus and l x + m y + n = 0 as directrix, the equation of the parabola is

#(x-alpha)^2+(y-beta)^2= (l x + m y + n )^2/(l^2 + m^2)#

If the focus is (a, 0) and the directrix is x + a = 0. this becomes

#(x-a)^2+y^2=(x + a )^2#. This simplifies to a standard form #y^2 = 4 a x#.

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