A parabolic mirror on a telescope has a focal length of 16 cm . a. For the coordinate system shown, write an equation of the parabolic cross section of the mirror. b. Determine the displacement of the mirror relative to the y -axis at the edge of the mirror. That is, find the x value at a point 12 cm above or below the vertex.
A parabolic mirror on a telescope has a focal length of 16 cm . a. For the coordinate system shown, write an equation of the parabolic cross section of the mirror. b. Determine the displacement of the mirror relative to the y -axis at the edge of the mirror. That is, find the x value at a point 12 cm above or below the vertex.
Solution Summary: The author calculates the parabolic cross section of the mirror for the given coordinate system using the standard equation of a parabola.
A parabolic mirror on a telescope has a focal length of
16
cm
.
a. For the coordinate system shown, write an equation of the parabolic cross section of the mirror.
b. Determine the displacement of the mirror relative to the
y
-axis
at the edge of the mirror. That is, find the
x
value at a point
12
cm
above or below the vertex.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY