badge image

Enroll For Free Now & Improve Your Performance.

User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

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

Please check your email for login details.

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

Total Price: Rs.

There are no items in this cart.
Continue Shopping
Grade: 12


given n straight lines and a fixed point O.through O a straight line is drawn meeting these points at R 1 ,R 2 ....,R n and a point R is taken on it such that, n/OR = 1/OR 1 + ......+ 1/OR n .show that locus of r is a straight line.

11 years ago

Answers : (1)

Ramesh V
70 Points

Let the n straight lines be : y=mix+ci  for i=1,2,3...n

let O be origin and R(h,k) be locus of R

equation of line OR is : y-mx=0 

so, k-mh=0

OR= (x2+y2)1/2

Ri = (ci/(m-mi), )

ORi = { (ci/(m-mi)*(1+m2)1/2 )

given n/OR = 1/OR1 + 1/OR2 + ....

n/(x2+y2)1/2 = (m-m1)/(c1*(1+m2)1/2) + (m-m2)/(c2*(1+m2)1/2) +............+(m-mn)/(cn*(1+m2)1/2)

on substituting k=mh above , we have

n/h = (k/h - m1)/c1 +   (k/h - m2)/c2+....                                                                          

n/h = k/h(1/c1 + 1/c2+ .....) - (m1/c1 + m2/c2+ ....)

put A=(1/c1 + 1/c2+ .....)

      B=(m1/c1 + m2/c2+ ....)

n/h = A*k/h - B

or n = kA - Bh               this is a straight line

or we can say its locus as Bx-Ay+n=0                                                         





11 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Course Features

  • 53 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details