Offset or Parallel Path to the Parabola | Steve Wait – April 4, 2019

y    = ax² (xy plane)

a    = coefficient
k    = .25a = focus (focus to vertex)
d    = twice the desired parallel or offset amount
x    = x coordinate on parabola
X_c = x offset value
y    = y coordinate on parabola
Y_c = y offset value

Parabola Offset / Parallel Path Compensation Equations (Ref. Fig. 1)

X_c = x ± (xd / (2√(4k²+x²)))

Y_c = y ± (kd / √(4k²+x²))

Fig. 1

Geogebra animation can be viewed here: Offset or “Parallel” Curve to the Parabola – GeoGebra

Tags: geometry