Asymptotes of Cruciform Curve

Theorem

The cruciform curve defined by the equation expressed in Cartesian coordinates as:

$x^2 y^2 = a^2 \paren {x^2 + y^2}$

has the following asymptotes:

\(\ds x\)

\(=\)

\(\ds \pm a\)

\(\ds y\)

\(=\)

\(\ds \pm a\)

Proof

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Sources

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