A Line at Fixed Angle to a Segment from a Fixed Point to a Fixed Line

Download Geometry Expressions File

A is at the origin, B on the line X=a. We take the envelope of the line through B at angle η to AB. The equation is complicated, but clearly a conic.

Copying and pasting shows the conic is a parabola, with focus at the origin and vertex as shown. We also see that the axis of the parabola makes angle θ with the original line.

Expressions

Name Input
Angle Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Focus Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Vertex Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Google Analytics Alternative