a normal cord of the parabolla y^2=4ax subtending a right angle at the vertex makes an acute angle with x axis,the angle is,,,,,,,,,,,,,,,,,,sir plz explain in detail

et 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

so    angel is  =tan^-1(√2)

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nd 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

so    angel is  =tan^-1(√2)

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you
the answer and detailed  solution very  quickly.