PARABOLAS
By: Brian Rayner
DEFINITION OF A PARABOLA
• “A parabola is the set of all points in a plane equidistant from a particular
line (the directrix) and a particular point (the focus) in the plane.” (Pearson
Pre-Calculus)
HISTORY OF PARABOLAS
• Menaechmus- Founder of the parabola.
• Apollonius- Named the parabola.
• Pappus- Found the focus and directrix of the parabola.
• Galileo- Studied properties of the parabola.
• Newton- Noticed that objects fall in parabolic paths.
PARTS OF A PARABOLA
• Directrix: A line used to determine the conic.
• Focus: Fixed point on the interior of a parabola used in the formal definition
of the curve.
• Axis: The line of symmetry for a parabola. The line passing through the focus
and perpendicular to the directrix.
• Vertex: The point where the parabola intersects its axis.
• Focal Length: The distance from the vertex to the focus of a parabola.
• Focal Width: The length of the chord through the focus and perpendicular to
the axis.
STANDARD EQUATIONS OF
PARABOLAS
• Standard equations for parabolas and the math used to find the values for
each part of the parabola.
PARABOLAS IN REAL LIFE
• Trajectory Motion
PARABOLAS IN REAL LIFE
• Architecture
PARABOLAS IN REAL LIFE
• Electronics
GOLDEN GATE BRIDGE
• Equation: Y = 0.000112x2 + 220
• Tower Heights: 500 feet
• Distance between towers: 4,200 feet
• Height above water: 220 feet