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68. Locus Definition of Parabola.notebook April 22, 2013
68. Locus Definition of a Parabola, Translated Parabolas, Applications, Derivation
scan page 430 all pictures
68. Locus Definition of Parabola.notebook April 22, 2013
Locus method of a lineA 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.
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
68. Locus Definition of Parabola.notebook April 22, 2013
For a parabola whose vertex is at the origin the equation is
y = x2 14p
(0, 0) vertex
(0, p) coordinate of the focus
y = p equation of the directrix
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
y = x237
y = x2 14p
Focus (0, ) Directrix y =
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)Directrix: y = p
y = x2 14p
scan p 432
68. Locus Definition of Parabola.notebook April 22, 2013
Now lets think about shifting the vertex.
vertex (h, k)
focus (h, k + p)
directrix: y = k p
axis of symmetry: x = h
Equation: y k = (x h)2 14p
p > 0 opens up p < 0 opens down
scan p 433
68. Locus Definition of Parabola.notebook April 22, 2013
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.
(h, k) (h, k+p)
y k = (x h)2 14p
directrix: y = kp
aos: x = h
68. Locus Definition of Parabola.notebook April 22, 2013
Parabolic reflectors are used in telescopes, microwave antennae, and searchlights.
scan p 434
68. Locus Definition of Parabola.notebook April 22, 2013
The reflecting surface of a parbolic antenna has the shape formed when the parabola y = x2 is rotated about the axis of symmetry.
120If the measurements are in feet, how
far from the vertex should the receiver be placed if it is to be at the focus?
a = 1 4p
68. Locus Definition of Parabola.notebook April 22, 2013
scan picture on page 435
Use the distance formula to find D1 and D2. D1 = D2
68. Locus Definition of Parabola.notebook April 22, 2013
68. Locus Definition of Parabola.notebook April 22, 2013
68. Locus Definition of Parabola.notebook April 22, 2013
68. Locus Definition of Parabola.notebook April 22, 2013