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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Page 1: 10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every

10-5 Parabola

Page 2: 10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every

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.

Page 3: 10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every

Page 4: 10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every

Page 5: 10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every

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

Page 6: 10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every

Page 7: 10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every

Change y2 – 2y-12+13 = 0 to standard form. Then find the vertex, foci, directrix and axis of symmetry.

Page 8: 10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every

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?

http://en.wikipedia.org/wiki/Parabola

http://en.wikipedia.org/wiki/Focus_(geometry)

http://en.wikipedia.org/wiki/Directrix_(conic_section)

http://en.wikipedia.org/wiki/Circle

http://en.wikipedia.org/wiki/Radius

http://en.wikipedia.org/wiki/Circles_of_Apollonius

http://en.wikipedia.org/wiki/Hyperbola

http://en.wikipedia.org/wiki/Ellipse

http://en.wikipedia.org/wiki/Circle

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