Trisectrix of Maclaurin has Asymptote

Theorem

Let $\TT$ be the trisectrix of Maclaurin embedded in a Cartesian plane with the equation:

$x^3 + x y^2 + a y^2 - 3 a x^2 = 0$

Then $\TT$ has one asymptote, which is the straight line $x = -a$.


Proof


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Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): trisectrix
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): trisectrix
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