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CONIC SECTIONS

CREATED BY: Amanda Holden


PARABOLAS F(x) = a(x-h)^2 + k A parabola is the locus of all points in a given plane that are the same distance from a given point, called the focus, and a given line, called the directrix. Car Headlights:


St. Louis Arch (Architecture):

McDonald’s Arch (Architecture):


Arch of a Slinky:


CIRCLES (x-h)^2 + (y-k)^2 = r^2 A circle is the locus of all points in a plane at a given distance, called the radius, from a fixed point on the plane, called the center. Mushroom Tops (Nature):

Center of a Flower (Nature):


Table Top:

Crop Circles (Nature):


ELLIPSES [(x-h)^2/a^2] + [(y-k)^2/b^2] = 1 An ellipse is the locus of all points in a plan such that the sum of the distances from two given points in the plane, called the foci, is constant. Tycho Brahe Planetarium in Copenhagen (Architecture):


Tilted Glass of Water:

Sanctuary Hall in the United States Capitol Building (Architecture):

Planets Orbiting the Sun:


Hyperbolas [(x-h)/a^2 – (y-k)/b^2] = 1 A hyperbola is the locus of all points in the plane such that the absolute value of the difference of the distances from two given points in the plane, called the foci, is constant.

Hourglass:


Legs of a Spider:

Stone Gate:

Black Bamboo Sculpture:


Conic Sections