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A property is given in my book which states that "if the tangent and normal at any point P of parabola meets the axes at T and G ,then ST=SG=SP" please tell what is S here

A property is given in my book which states that "if the tangent and normal at any point P of parabola meets the axes at T and G ,then ST=SG=SP" please tell what is S here

Grade:12th pass

1 Answers

Vinay Mehta
13 Points
2 years ago
S is the focus of parabola. Hope u get it now,how they are equal.Therefore
The equation of tangent is yt=x+at^2 it cuts the x axis at -at^2 Therefore ST= a+at^2 similarly SG= a+at^2 and SP equals to perpendicular dist of point P from directrix SP= a+at^2.
Finally ST=SP=SG

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