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# 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:

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: