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Locus

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The Ellipse

The Parabola

The Hyperbola

General Form

Intersections of Lines & Conics

Summary&Test

  

jdsmathnotes

 

UNIT 9 : THE CONICS

LESSON 4: THE PARABOLA

Definition: Given a fixed point F and a fixed line d in the plane. A parabola is the locus (set) of points P in the plane, each of which is equidistant from the

fixed point F (the focus) and the fixed line d (the directrix). In the diagram |PF| = |PD| for any point P on the parabola.

The vertex V is the midpoint of the perpendicular line segment from the focus F to the directrix d .

 

 

 

 

 

 

Example 1

 

 

 

 

 

Example 2:

 

 

 

 

 

Example 3:

 

 

 

 

 

 

 

 

 

 

Text Box: Main Ideas for the Parabola:
	 |PF| = |PD|  for any point P on the parabola.
	The vertex is halfway between the focus and directrix
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Definition:

  1. A chord is a line segment whose end points are on the curve.
  2. A focal chord is a chord that passes through the focus.
  3. The focal length is the distance from the vertex to the focus [VF]

 

 

Example 4:

Given the parabola with equation x2 = -8y,

a)      Find the focus and equation of the directrix.

b)      Sketch the graph and state the focal length.

c) Find the length of the focal chord [AB] perpendicular to the

axis of symmetry of the parabola. This length is called the

focal width.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Example 5:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Example 6:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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