White PlainsHigh School
Mr.Stanton
PCH 8.2 Conic Sections - Parabolas
SWBAT use the focus-directrix form of an Equation of a Parabola
Parabola – The set of all points in a plane, that are equidistant from…
a fixed point (the focus) and a fixed line (the directrix).
A line passing through the focus and ⊥ to the directrix is the ______
Case #1: Parabola, axis of symmetry is the x-axis, opens to the right.
Distance from F to P = Distance from P to D
Equations of a Parabola, Vertex at (0,0); Focus on an Axis; a>0
Vertex / Focus / Directrix / Equation / Description(0,0) / (a,0) / / / Opens Right
(0,0) / (-a,0) / / / Opens Left
(0,0) / (0,a) / / / Opens Up
(0,0) / (0,-a) / / / Opens Down
Derive the equation for Case #3 from the table above.
Example 1
Find the equation of a parabola with vertex (0,0) and focus (3,0). Graph the equation, by hand, no calculator, using a minimum of three points.
A segment parallel to the directrix whose midpoint is the focus and whose endpoints on a parabola is called the ______.
How is the length of this segment related to the equation of the parabola?
Example 2
Discuss (i.e. provide exhaustive information about) the equation
Example 3
Find the equation and sketch the graph of a parabola with focus (0, 4) and directrix y=-4.
Example 4
Find the equation of a parabola with vertex (0, 0) and axis of symmetry = x-axis that passes through . Indicate on your graph the focus and directrix.
DAY 2
SWBAT use the focus-directrix form of an Equation of a Parabola for Parabolas when vertex is not at the origin.
Draw 4 parabolas with vertices NOT at the origin that match the 4 descriptions below. Be sure to indicate the location of each focus and directrix
Equations of a Parabola, Vertex at (h,k); Axis of Symmetry Parallel to an Axis; a>0
Vertex / Focus / Directrix / Equation / Description(h,k) / ( ) / / Opens Right
(h,k) / ( ) / / Opens Left
(h,k) / ( ) / / Opens Up
(h,k) / ( ) / / Opens Down
Example 5
Find the equation of a parabola with vertex (-2, 3) and focus (0, 3). Graph the equation by hand.
Example 6
Fully discuss the equation . Graph the equation by hand.
A Paraboloid of Revolution is formed when a parabola is rotated around its axis of symmetry
Example 6
A satellite dish is a paraboloid of Revolution. The signals the dish receives are collected in a single location. If the dish is 4 feet across and is 3 inches deep at its center, where should the receiverbe placed?
Araceibo Radio Telescope, Puerto Rico. 305m dish, fixed in a natural bowl
VLA (Very Large Array) in Socorro, New Mexico consists of 25 separate telescopes (each of 25m diameter) arranged in the shape of the letter Y, with each arm of the Y being 21 km long. The array is equivalent to a single radio telescope with a dish of 42 km diameter.