Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Q1 If PN is the perpendicular from a point on a rectangular hyperbola to its asymptotes, the locus, the midpoint of PN is a/an Q2 The product of perpendiculars from any point on the hyperbola having general equation to is asymptotes is equal to? 2 If PN is the perpendicular from a point on a rectangular hyperbola to its asymptotes, the locus, the midpoint of PN is a/an

 





  Q1 If PN is the perpendicular from a point on a rectangular hyperbola to its asymptotes, the locus, the midpoint of PN is a/an


Q2

 The product of perpendiculars from any point on the  hyperbola   having general equation  to is asymptotes is equal to?




2 If PN is the perpendicular from a point on a rectangular hyperbola to its asymptotes, the locus, the midpoint of PN is a/an


Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Zahid

let equation of hyperbola is   x2 -y2 =a2

 and equation os aymptote is  :   y=x   (slope  m=1)

let N(x1,x1) on the asymptote ,and a point P(asecθ ,atanθ) on the hyperbola and(h,k) is the mid point of PN

 h=(x1+asecθ)/2   or  asecθ =2h-x1 ...............1

k = (x1+atanθ)/2  or  atanθ =2k-x1 ................2

 

since PN is perpendiculat to aymptote so slope of PN =-1

 (k-x1)/(h-x1)=-1

 x1 =(h+k)/2

so put this value in equation 1 and 2

 asecθ=(3h-k)/2

 atanθ =(3k-h)/2

 

now square and subtract

 a2(sec2θ -tan2θ) = {(3h-k)/2}2 - {(3k-h)/2}2

 a2 = {(3h-k)/2}2 - {(3k-h)/2}2

 4a2 =8(h2-k2)

 h2-k2=a2/2

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
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