Guest

Find the locus of midpoint of variable chord of parabola y 2 = 4ax such that tangents make an angle Φ between them.

Find the locus of midpoint of variable chord of parabola y2 = 4ax such  that tangents make an angle Φ between them.

Grade:

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear Priyansh

let the mid point is (h,k)

and let the point where tangent touch the parabola is (at12,2at1) and (at22,2at2)

 

so 2h = a(t12 + t22)    and  2k = 2a(t1+t2)   ...................1

 

from equation 1 find the value of t1t2 = (k2 -2ha)/2a2

and |t1-t2| = 1/a {k2 - 4ha}1/2

so given tanΦ = |m1-m2|/(1+m1m2)

where m1 = 1/t1

            m2 =1/t2

 

so put these value

tanΦ =2a{k2 -4ha}1/2 / {k2 -2ha}


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
Badiuddin

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free