Parabola3

If y1,y2 are the ordinates of the two points P and Q on the parabola and y3 is the ordinate of the point of intersection of tangents at P and Q,then

y1,y2,y3 are in AP.Prove

1 Answers

y²=4ax

dy/dx=2a/y = 1/t

so y=1/t x + at

and y=1/m x + am

Solve them simulatenously,

(m-t)/mt x = a(m-t)

so x=a/mt

hence, y=a(1/m+1/t)

The originial ordinate were 2a/m and 2a/t

Hence the ordinate of the point of intersection is the AM of 2a/m and 2a/t

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