Normal Lines to a Parabola

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The normal line to the graph of parabola at the point
,
is
, or equivalently
. The number of real roots of a reduced cubic
depends on the sign of
. So the number of normal lines to
through
depends on the sign of
. If
, there is one normal line to
through
; if
, there are two normal lines; and if
, there are three. (For the cusp
, the only normal line is
.)
Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Reference: D. Sanchez and K. C. Smith, "Normal Lines and the Evolute Curve," The College Mathematics Journal, 31(5), 2000 pp. 397–403.
Permanent Citation
"Normal Lines to a Parabola"
http://demonstrations.wolfram.com/NormalLinesToAParabola/
Wolfram Demonstrations Project
Published: March 7 2011