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Notice: The vertical
parabola has its focus at (0,2), it’s directrix is at y=-2, and the equation is
8y=x2. The horizontal
parabola has its focus at (1,0), its directirx is at x=1, and the equation is
4x=y2. 1) Make sure the room is somewhat dark. 2) Turn on the two flashlights and hold them both so that their light rays are perpendicular to the directrix.
3) Watch the light reflect to the focus! 4) Try the same thing with the horizontal parabola! Why does this work? This works because of the fact that since every point on the parabola is equidistant to the focus and the directrix, when a light ray hits the parabola perpendicular to the directrix, it will reflect off towards the focus. Study Guide 1) Where do all parallel rays bounce off the parabola to? 2) What is the invisible line whose points are always equally as far from a point on the parabola as the focus? 3) Why is the second parabola horizontal (hint, see equation)? 4) In the quadratic equation (equation of a parabola), 4p(y-k)=(x-h)2, p is the distance from the vertex (origin of the parabola) to the focus, and (h,k) is the center or vertex. In the two parabolas in this exhibit, find p, k, and h. 5) As the focus gets further and further away from the center, would the parabola become thinner or wider? 6) If the light rays hitting the parabola
were not perpendicular to the directrix, would they still reflect to the
focus? (Try shining the flashlights
towards the parabola at different angles.) Parabolic Reflectors Main Page
Parabolic Reflectors Study Guide |
