Parabolas. Section 8.3. You have studied parabolas in several different lessons, and you have transformed parabolic graphs to model a variety of situations. Now a locus definition will reveal properties of parabolas that you can use to solve other practical problems.
You have studied parabolas in several different lessons, and you have transformed parabolic graphs to model a variety of situations.
Satellite dishes, used for television, radio, and other communications, are always parabolic.
The designs of telescope lenses, spotlights, satellite dishes, and other parabolic reflecting surfaces are based on a remarkable property of parabolas:
A paraboloid is a three-dimensional parabola, formed when a parabola is rotated about its line of symmetry.
A parabola is the set of points for which the distances d1 and d2 are equal.
The directrix can also be neither horizontal nor vertical, creating a parabola that is rotated at an angle.
You can use this information and the distance formula to find the value of f when the vertex is at the origin.
If the parabola is vertically oriented, the x- and y-coordinates are exchanged, for a final equation of
Consider the parent equation of a horizontally oriented parabola, y2 = x.
Use the standard form, y2 =4fx, to locate the focus and the directrix of y2 = x.