let agiven line L1 intersect the x and y axis at P &Q respectively.Let another line L2 perpendicular L1 cut the x and y axis at R & S respectively.Show that the locus of the point of intersection of the lines PS & QR is a circle passing through the origin.

4 years ago

Share

Answers : (1)

                                        

let given line is L1: y=mx+c


(P,Q)=(-c/m,0) , (0,c)


now L2 is perpendicular to line L1


slope of L2*slope of L1=-1            (m1m2=-1)


 eq of L2: y=-x/m + k                 (k is any variable)


(Q,R)=(km,0),(0,k)


eq of PS is y=mkx/c + k and.................1


eq of QR is  y=-x/km + c ...................2


let the point if intersection be (X,Y)


 after solving 1 and 2


X= (c-k)/(mk/c + 1/mk )...............3


Y= (km+1/m) /(mk/c + 1/mk)...........4


 eliminate k by solving eq 3 and 4 you will get the equation in terms of X,Y and c .......this will give the required locus which is circle passing through origin...

4 years ago

Post Your Answer

More Questions On IIT JEE Entrance Exam

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
can iit advance marks be used to get into best NIT’s
 
 
No... It has clearly been mentioned in the brochure the criteria for NIT. through central counselling. So JEE mains would be considered and not advanced for admission to NIT’s...
  img
Ravi one month ago
 
  img
Aziz Alam one month ago
The radius of the circle having centre at (2,1) and whoseone of the chord is diameter of the circle x 2 + y 2 – 2x – 6y + 6 =0 is??Sir please explain!!
 
 
let the radius of circle be r then equation of circle (x-2) 2 +(y-1) 2 =r 2 x 2 +y 2 -4x-2y+5-r 2 =0...................1 x 2 +y 2 -2x-6y+6=0........................2 common chord of circle 1...
  img
Sunil Raikwar 4 months ago
Maths short tips and trcks
 
 
Hi, There is no tricks of tips as such in mathematics. The more problems you solve the more short methods ull get to solve a question. Do not rely on tricks coz many questions are desigend...
  img
Yash Baheti 3 months ago
I am a beginner, so should i practice from S.k. goyal- Algebra Or its its a bit high level???
 
 
S.K.Goyal does have a good set of questions and for a beginner it does seems to be a bit tough but if you have the patience , then you should actually sit with it and solve those problems...
  img
Aziz Alam 4 months ago
 
Then from which books should i study to get a good set of questions as a beginner & sir please justify specific names and dont post the link as there are too many books there..........@ AZIZ...
 
Sankalp Tiwari 4 months ago
Which is the birth place of Hitler? In which year did Hitler become the Chancellor of Germany?
 
 
Adolf Hitler (20 April 1889 – 30 April 1945) was an Austrian-born German politician and the leader of the National Socialist German Workers Party (German: Nationalsozialistische...
 
Vijay Luxmi Askiitiansexpert 5 years ago
Please compare NIT warangal and NIT calicut. Which is better?
 
 
Hi Student, NIT Waranagal is better in terms of placements and campus...
  img
Harishwar one month ago
 
you can check branchwise closing, college wise branches, branchwise intake and all other detail of all NIT from CSAB android app. you can download it by searching CSAB in play store. similar...
 
Nitin Rola one month ago
View all Questions »