Physical meaning of directrix?

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In summary, the conversation discusses the concept of a directrix in relation to conic sections and questions the physical significance of it. The idea of unifying the conics through the ratio of distances from a point to the focus and the directrix is mentioned, but the conversation wonders if there is a deeper, more physical explanation. The use of Dandelin spheres to explain directrices in all conics is suggested as a potential explanation.
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homology
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I suddenly realized that the very notion of a directrix seems odd to me.

(1) I don't know any physical significance of such a thing

(2) How anyone came to define the parabola as such

Any help? I read some older posts about the history of the directrix/focus definitions of the conic sections and I can see the idea of unifying the conics through the ratio of distances from a point to the focus and from the point to the directrix but perhaps there is something more, something deeper, something physical?

Cheers,

Kevin
 
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Related to Physical meaning of directrix?

1. What is the physical meaning of a directrix?

The directrix is a line that is used to define a parabola. It is the fixed line that is parallel to the axis of symmetry of the parabola. The physical meaning of a directrix is that it represents the path of a light ray that is reflected off the parabola's surface.

2. How does a directrix affect the shape of a parabola?

The directrix influences the shape of a parabola by determining the position of its vertex and the direction in which the parabola opens. The distance between the vertex and the directrix also affects the curvature of the parabola's arms.

3. Can a directrix be located on any side of a parabola?

Yes, a directrix can be located on either side of a parabola. The only requirement is that it must be parallel to the axis of symmetry. However, in most cases, the directrix is positioned below the parabola, as this yields a parabola that opens upward.

4. How does the directrix relate to the focus of a parabola?

The focus of a parabola is a point on the parabola's axis of symmetry that is equidistant from the directrix and the vertex. In other words, the focus is the point where all of the reflected light rays converge after reflecting off the parabola's surface.

5. Can the directrix of a parabola be changed?

Yes, the directrix of a parabola can be changed by simply altering its position or orientation. This can be done by adjusting the value of the directrix's equation or by physically moving the line. Changing the directrix will result in a different parabola with a different vertex, focus, and shape.

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