Solar cookers provide an alternative form of cooking in regions of the world where consistent sources of fuel are not readily available. Suppose that a 36 -in . solar cooker has parabolic cross sections. A coordinate system is chosen with the origin placed at the vertex of a cross section through the center of the mirror. The equation of the parabola is modeled by x 2 = 82 y , where x and y are measured in inches a. Where should a pot be placed to maximize heat? That is, where is the focus? b. Determine the equation of the directrix.
Solar cookers provide an alternative form of cooking in regions of the world where consistent sources of fuel are not readily available. Suppose that a 36 -in . solar cooker has parabolic cross sections. A coordinate system is chosen with the origin placed at the vertex of a cross section through the center of the mirror. The equation of the parabola is modeled by x 2 = 82 y , where x and y are measured in inches a. Where should a pot be placed to maximize heat? That is, where is the focus? b. Determine the equation of the directrix.
Solution Summary: The author calculates the distance of where the receiver should be placed to maximize the signal strength, that is, where there is focus.
Solar cookers provide an alternative form of cooking in regions of the world where consistent sources of fuel are not readily available. Suppose that a
36
-in
.
solar cooker has parabolic cross sections. A coordinate system is chosen with the origin placed at the vertex of a cross section through the center of the mirror. The equation of the parabola is modeled by
x
2
=
82
y
,
where
x
and
y
are measured in inches
a. Where should a pot be placed to maximize heat? That is, where is the focus?
b. Determine the equation of the directrix.
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