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

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 |
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