10-5 parabola. parabola – “u” shape formed by quadratics. created but all points equal...
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10-5 Parabola
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Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix.
Every parabola has an axis of symmetry and vertex.
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focal width. A focal width is the length of a vertical or horizontal line that passes through the focus and touches the parabola on each end. Width = l 4p l
Find the focal width of a parabola with equation y2 = 16x
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Change y2 – 2y-12+13 = 0 to standard form. Then find the vertex, foci, directrix and axis of symmetry.
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Locus: A set of points that satisfy a given set of conditions.
All conic sections can be define use locus.
– Parabola: the set of points equidistant from a single point (the focus) and a line (the directrix).
– Circle: the set of points for which the distance from a single point is constant (the radius). The set of points for each of which the ratio of the distances to two given foci is a positive constant (that is not 1) is referred to as a Circle of Apollonius.
– Hyperbola: the set of points for each of which the absolute value of the difference between the distances to two given foci is a constant.
– Ellipse: the set of points for each of which the sum of the distances to two given foci is a constant. In particular, the circle is a locus.
Did you know…you can determine a shape by the value of e?