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Parabola Project

History of the Parabola

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Introduction
History
Real Life Uses
The Conic Sections

  • Menaechmus (380 BC - 320 BC) found the parabola

  • Apollonius (262 BC - 190 BC) named the parabola

  • Pappus (290 - 350) found the focus and directrix of the parabola

  • Galileo (1564 - 1642) saw that objects falling due to gravity due so in parabolic paths

  • Gregory (1638 -1675) studied properties of the parabola

  • Newton (1638 - 1675) studied properties of the parabola




  • Definition:
    A parabola is is a set of all points that are the same distance from a fixed line (directrix) and a fixed point (focus)not on the directrix



    Equation: Standard Form when directrix is parallel to the y-axis:

    (y-k) = 4p(x-h)

    Standard Form when directrix is parallel to the x-axis:

    (x-h) = 4p(y-k)




  • When p is positive, the parabola opens upwards

  • When p is negative, the parabola opens downwards

  • When h is negative, it moves to the left of the orgin. When h is positive, it moves to the right of the orgin.

  • When k is negative, it moves towards the bottom of the graph. When k is positive, it moves towards the top of the graph.

When P is negative
np.gif

When P is positive
pp.gif

The affects of K
k.gif

The affects of H
h.gif