Envelope of Hypotenuse of Right Angled Triangle, whose short sides add up to a constant

Download Geometry Expressions File

Set the short sides along the axes with lengths a and k-a. The equation is clearly a conic, and in fact a parabola:

We see its focus and vertex.

Expressions

Name Input
Point H Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Point G Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Envelope Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image