Question

What is the directrix of a parabola?

Answer 1

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`.