Texas Instruments TI-83 Plus User Manual page 37

Example
A lamp with an opaque cylindrical shade 1.5 feet in diameter, 2
feet high has a light bulb located at the center of the shade. It
casts a shadow, which is of the form of a hyperbola, on a wall 3
feet from the bulb and parallel to the shade. Assume the origin is
at the light bulb. Find the vertices, foci, and slope of the
asymptotes of the hyperbola.
Steps:
The equation of the cone of light is
The equation of the wall is: Z = 3.
1. Substitute z into the equation and solve:
2
16X
9
2
16X
9
16X
2
Y
2
Y
16
TI-83 Plus Conic Graphing
2
16(3)
2
+ Y = 0
9
2
Y = -16
2
= 16
9
2
X
9 = 1
16X 16Z
2 2
+
9 9
Y = 0.
2
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