A beautiful Parabolaaas

Geometry Level 3

A parabola \(y^2=4ax\) is drawn. Through two points , say 'P' and 'Q' on parabola which are also on latus rectum of that parabola , two lines are drawn which intersect at origin 'O'. so triangle POQ is formed. Now through points 'P' and 'Q' their normals are interscted at point 'R'. Now , through point 'R' , as a vertex another similar parabola is drawn in same direction. The points on latus rectum on this second parabola form triangle with origin . and similarly many parabolas are drawn. So, which parabola will have area of triangle formed in similar way, 1156 times the first one.


  1. Always triangles are formed by the points on latus rectum of corresponding parabola and origin 'O'.

  2. New parabola is drawn whose vertex is at the point of intesction of normals drawn to points on latus rectum of previous one.


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