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How can I graph the set of all scalar multiples of the points on the surface $(x,x^3,1)$, that is, $\{(t(x, x^3, 1)\mid t,x\in \mathbb R\}$ in mathematica? I tried

ParametricPlot3D[{t*x, t*x^3, t}, {t, -10, 10}, {x, -10, 10}]

but it gave me an incomprehensible thin, long strip of something.

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    $\begingroup$ Scale the units of the x range. (E.g., look at the result with {x,-1,1}. $\endgroup$
    – Alan
    Commented Nov 10, 2022 at 23:08

1 Answer 1

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Use Manipulate and set BoxRatios -> 1.

Manipulate[
 ParametricPlot3D[t {x, x^3, 1}, {t, -a, a}, {x, -b, b}, 
  BoxRatios -> 1, PerformanceGoal -> "Quality", 
  PlotRange -> All], {{a, 1}, -1000, 1000}, {{b, 1}, -1000, 1000}]
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