The Association of Mathematics Teachers had organized a seminar for mathematics teachers in your region. The theme of the seminar is on conic sections and their application to real life. Inclusive of the registration fee are meals and snacks, a program, training kits, and a T-shirt. The association desires to come up with a common computer-generated graphics design for the front cover page of the program, tarpaulin for the stage, and the T-shirts. The details of the design feature the equations and graphs of conic sections, and their practical applications to life situations. You are one of the famous designer/graphic artists in your province. Knowing your expertise in mathematics, you were contracted by the association to create a design for each of the three mentioned aspects of the seminar.
Conic Sections as T-shirt Design
Task/s:
1. Create a sketch/draft of your design containing characteristics (graphs, equations, properties) of any conic sections.
2. The design should include the title of the seminar, theme, date, and venue. You are free to position the text with respect to the design that you have created,
3. There should be at most five colors used in the design.
4. Output must be in a long bond paper.
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Answer:
Key Points
A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane; the three types are parabolas, ellipses, and hyperbolas.
A conic section can be graphed on a coordinate plane.
Every conic section has certain features, including at least one focus and directrix. Parabolas have one focus and directrix, while ellipses and hyperbolas have two of each.
A conic section is the set of points
P
whose
distance to the focus is a constant multiple of the distance from
P
to the directrix of the conic.
Key Terms
vertex: An extreme point on a conic section.
asymptote: A straight line which a curve approaches arbitrarily closely as it goes to infinity.
locus: The set of all points whose coordinates satisfy a given equation or condition.
focus: A point used to construct and define a conic section, at which rays reflected from the curve converge (plural: foci).
nappe: One half of a double cone.
conic section: Any curve formed by the intersection of a plane with a cone of two nappes.
directrix: A line used to construct and define a conic section; a parabola has one directrix; ellipses and hyperbolas have two (plural: directrices).