Conic Applications in the Real World A sample presentation by Mrs. Kohler.
-
Upload
gael-hassell -
Category
Documents
-
view
215 -
download
2
Transcript of Conic Applications in the Real World A sample presentation by Mrs. Kohler.
Conic Applications in the
Real WorldA sample presentation
by Mrs. Kohler
Circles
(x−h)2 + (y−k)2 =r2
Center: (h, k)
Radius: r
Circles: A Roulette Table
• One application of a circle is a Roulette Table.
• The spinning of the wheel keeps
the ball on the rim. • Slower spinning lessens the
centrifugal force and the ball drops in a slot.
Ellipses
(x−h)2
a2 +(y−k)2
b2 =1
Center: (h, k)
Foci Formula:(where a > b)
c2 =a2 −b2
Ellipses: The Solar System
• One application of the ellipse is the orbits of the planets in our solar system.
• The sun represents one of
the foci.
Parabolas
Vertical ParabolasVertex: (h, k)
Focus: (h, k+c)Directrix: y = k – c
(y−k) =a(x−h)2 or (x−h) =a(y−k)2
Horizontal ParabolasVertex: (h, k)
Focus: (h+c, k)Directrix: x = k – c
Parabolas: A Light Filament
• One application of a parabola is the filament in a flashlight.
• The mirrors on the filament
cause the reflection of the bulb to shine outward.
Hyperbola
(x−h)2
a2 −(y−k)2
b2 =1
Horizontal HyperbolaVertex: (h, k) Foci: (h+c, k) (h–c, k)
c2 =a2 +b2
or(y−k)2
a2 −(x−h)2
b2 =1
Vertical HyperbolaVertex: (h, k) Foci: (h, k +c) (h, k–c)
Foci Formula
Hyperbolas: Underwater Radar
• One application of a hyperbola is the LONAR radar system.
• This technology is used in submarines. This device detects the intersection of sound waves.
• The intersection points create a
hyperbola.