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Math Help - graphing a cylinder

  1. #1
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    Question graphing a cylinder

    Hi,

    Please teach me how to graph a cylinder ( please show me the step of graphing). Thank you very much.

    4x^2 + y^2 = 9
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  2. #2
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    Hello, kittycat!

    Please teach me how to graph a cylinder: . 4x^2 + y^2 \:= \:9

    Since x is not in the equation, z is unrestricted.
    . . The z-values are on (-\infty,\,\infty)
    The graph extends "up" and "down" infinitely.

    When z=0, we have the trace of the cylinder on the xy-plane
    . . . . . the "floor" of the coordinate system.

    This trace is: . 4x^2 + y^2 \:=\:9\quad\Rightarrow\quad\frac{x^2}{\frac{9}{4}} + \frac{y^2}{9} \:=\:1

    This is an ellipse with major axis 6 in the y-direction
    . . and minor axis 3 in the x-direction.

    Sketch this ellipse on the xy-plane (the "floor")
    . . then draw the cylinder "straight up" and "straight down".

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