What is the directrix of a parabola?

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What is the directrix of a parabola?

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Answer 1 · 2016-05-10T05:47:03

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 $(α, β)$ $(alpha, beta)$ as focus and l x + m y + n = 0 as directrix, the equation of the parabola is

${(x - α)}^{2} + {(y - β)}^{2} = \frac{{(l x + m y + n)}^{2}}{l^{2} + m^{2}}$ $(x-alpha)^2+(y-beta)^2= (l x + m y + n )^2/(l^2 + m^2)$

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

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

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What is the directrix of a parabola?

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