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The normal chord at a point `t` on the parabola y^2=4ax subtends a right angle at the vertex then t^2 is equal to what?

The normal chord at a point `t` on the parabola y^2=4ax subtends a right angle at the vertex then t^2 is equal to what?

Grade:11

1 Answers

Arun
25758 Points
4 years ago
 

Dear Sunny

 

let end point of the chord is (at12 ,2at1) and (at22 ,2at2)

 

since it is normal to parabola  so t2 = -t1  - 2/t1

 

equation of normal of parabola    y  =-tx + 2at + at3

 

  slope is  -t1   which is given acute  so -t1 >0

 

or  t1

 

now chord make right angel at origin   so    {(2at1 -0)/ (at12 -0)}{(2at1 -0)/ (at12 -0)} =-1

 

t1t2 =-4

 

  t1(-t1  - 2/t1) =-4

 

 t1 =-√2

 

Hence 

t² = 2

 

Regards

Arun (askIITians forum expert)

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