Three Points on a Parabola

Let three points A, B, C lie on a parabola with axis OO'. Let AA', BB', CC' be parallel to the axis. Form intersections

  P = AB ^ CC',
Q = AC ^ BB'
R = BC ^ AA'.

Let the tangents to the parabola at A and B meet at MC, those at A and C meet at MB, and the tangents at B and C meet at MA.

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Prove that

  1. MA lies on PQ, MB on PR, and MC on QR.
  2. PQ is parallel the tangent at A, PR at B, and QR at C.

Conic Sections > Parabola

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