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.