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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

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

Grade:12

4 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear jauneet

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 <0

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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Badiuddin

sid
22 Points
7 years ago
Can you please explain geometrically this question .I am very confuse about how to draw its figure.
ankit singh
askIITians Faculty 614 Points
3 years ago

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)

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.
We are all IITians and here to help you in your IIT JEE preparation.
All the best.
Regards,
Askiitians Experts

ankit singh
askIITians Faculty 614 Points
3 years ago

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.

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