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.
|What if applet does not run?|
- MA lies on PQ, MB on PR, and MC on QR.
- PQ is parallel the tangent at A, PR at B, and QR at C.
Conic Sections > Parabola
- The Parabola
- Archimedes Triangle and Squaring of Parabola
- Focal Definition of Parabola
- Focal Properties of Parabola
- Geometric Construction of Roots of Quadratic Equation
- Given Parabola, Find Axis
- Graph and Roots of Quadratic Polynomial
- Greg Markowsky's Problem for Parabola
- Parabola As Envelope of Straight Lines
- Generation of parabola via Apollonius' mesh
- Parabolic Mirror, Theory
- Parabolic Mirror, Illustration
- Three Parabola Tangents
- Three Points on a Parabola
- Two Tangents to Parabola
- Parabolic Sieve of Prime Numbers
- Parabolic Reciprocity
- Parabolas Related to the Orthic Triangle