Envelope of Hypotenuse of Right-angled Triangles of Constant Area

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To generate area k, we use one short side length a, the other length 2k/a. Clearly the locus is a hyperbola. We can find its foci by drawing a hyperbola and giving it the equation of the locus.

Expressions

Name Input
Focus 2 Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Locus Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Focus 1 Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image