1. 68. Locus Definition of Parabola.notebook April 22, 2013
68. Locus Definition of a Parabola, Translated
Parabolas, Applications, Derivation
scan page 430 all pictures
2. 68. Locus Definition of Parabola.notebook April 22, 2013
Locus method of a line
A line is the locus of all the points equidistant from 2 points.
A circle is the locus of all points that are equidistant from the center.
3. 68. Locus Definition of Parabola.notebook April 22, 2013
Parabola the locus of all points that are equidistant
from a given point (focus) and a given line (directrix)
scan pics p 431
4. 68. Locus Definition of Parabola.notebook April 22, 2013
For a parabola whose vertex is at the origin the equation is
1 2
y = x
4p
(0, 0) vertex
(0, p) coordinate of the focus
y = p equation of the directrix
5. 68. Locus Definition of Parabola.notebook April 22, 2013
1. Find the coordinates of the focus and the equation of the directrix for the parabola
3 2
y = x 1 2
y = x
7 4p
Focus (0, ) Directrix y =
6. 68. Locus Definition of Parabola.notebook April 22, 2013
2. The focus of a parabola has coordinates (0, 5/3) and the vertex
is at the origin. Find the equation of the parabola and sketch it.
Focus: (0, p) 1 2
y = x
Directrix: y = p 4p
scan p 432
7. 68. Locus Definition of Parabola.notebook April 22, 2013
Now lets think about shifting the vertex.
vertex (h, k)
focus (h, k + p) Equation: y k = (x h)2
1
4p
directrix: y = k p
axis of symmetry: x = h p > 0 opens up p < 0 opens down
scan p 433
8. 68. Locus Definition of Parabola.notebook April 22, 2013
(h, k) (h, k+p)
3. A parabola has a vertex of (2, 1) and focus (2, 1). Write the equations for
the parabola, the directrix, and the axis of symmetry. Sketch the parabola.
y k = (x h)2
1 directrix: y = kp
4p
aos: x = h
10. 68. Locus Definition of Parabola.notebook April 22, 2013
1
The reflecting surface of a parbolic antenna has the shape formed when the parabola y = x2
is rotated about the axis of symmetry. If the measurements are in feet, how 20
far from the vertex should the receiver be placed if it is to be at the focus?
a = 1
4p
