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UNIT 10 : 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:
- A chord is a line segment whose end points are on the curve.
- A focal chord is a chord that passes through the focus.
- 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:
