Solving Application Problems with Conic Sections
Understand and apply concepts of conic sections to solve real-world problems. Examples include determining parabolic reflector equations, locating light bulb filaments, positioning whispering dishes in a whispering gallery, and finding possible airplane locations using hyperbolas.
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Applications of Conics ES: Demonstrate understanding of concepts Obj: Be able to solve application problems which utilize conic sections. https://www.youtube.com/watch?v=C161yzFMTVg
A searchlight has a parabolic reflector (has a cross section that forms a bowl ). The parabolic bowl is 16 inches wide from rim to rim and 12 inches deep. The filament of the light bulb is located at the focus. (a) What is the equation of the parabola used for the reflector? (b) How far from the vertex is the filament of the light bulb?
Two girls are standing in a whispering gallery that is shaped like semi- elliptical arch. The height of the arch is 30 feet, and the width is 100 feet. How far from the center of the room should whispering dishes be placed so that the girls can whisper to each other? (Whispering dishes are places at the foci of an ellipse).
Two radar sites are tracking an airplane. The first radar site is located at (0, 0), and shows an airplane to be 200 miles away. The second radar site, located 160 miles east of the first, shows the airplane to be 100 miles away. Find the coordinates of all possible points where the airplane could be located. (Find the equation of the hyperbola where the plane could be located).
