Request a call back

Join NOW to get access to exclusive study material for best results

JEE Class main Answered

Sir please solve every step for this question 
question image
Asked by Surjitsp6u | 03 Sep, 2019, 22:48: PM
answered-by-expert Expert Answer
Let the equations of n straight lines be
y=mix+ci for i=1,2,3,...n
Let O be the origin and R(h,k) as the locus of R
Equation of the line OR is y=mx
i.e. k-mh=0
N o w comma space O R equals square root of h squared plus k squared end root
R subscript i equals open parentheses fraction numerator c subscript i over denominator m minus m subscript i end fraction comma m cross times fraction numerator c subscript i over denominator m minus m subscript i end fraction close parentheses
O R subscript i equals square root of open parentheses fraction numerator c subscript i over denominator m minus m subscript i end fraction close parentheses squared plus open parentheses fraction numerator m c subscript i over denominator m minus m subscript i end fraction close parentheses squared end root equals open parentheses fraction numerator c subscript i over denominator m minus m subscript i end fraction close parentheses square root of 1 plus m squared end root
G i v e n space t h a t colon
fraction numerator n over denominator O R end fraction equals fraction numerator 1 over denominator O R subscript 1 end fraction plus fraction numerator 1 over denominator O R subscript 2 end fraction plus... plus fraction numerator 1 over denominator O R subscript n end fraction
fraction numerator n over denominator square root of h squared plus k squared end root end fraction equals fraction numerator m minus m subscript 1 over denominator c subscript 1 square root of 1 plus m squared end root end fraction plus fraction numerator m minus m subscript 2 over denominator c subscript 2 square root of 1 plus m squared end root end fraction... plus fraction numerator m minus m subscript n over denominator c subscript n square root of 1 plus m squared end root end fraction
S u b s t i t u t i n g space k equals m h
rightwards double arrow fraction numerator n over denominator h square root of 1 plus m squared end root end fraction equals fraction numerator begin display style k over h end style minus m subscript 1 over denominator c subscript 1 square root of 1 plus m squared end root end fraction plus fraction numerator begin display style k over h end style minus m subscript 2 over denominator c subscript 2 square root of 1 plus m squared end root end fraction... plus fraction numerator begin display style k over h end style minus m subscript n over denominator c subscript n square root of 1 plus m squared end root end fraction
rightwards double arrow n over h equals fraction numerator begin display style k over h minus m subscript 1 end style over denominator c subscript 1 end fraction plus fraction numerator begin display style k over h minus m subscript 2 end style over denominator c subscript 2 end fraction... plus fraction numerator begin display style k over h minus m subscript n end style over denominator c subscript n end fraction
rightwards double arrow n over h equals k over h open parentheses 1 over c subscript 1 plus 1 over c subscript 2 plus.... plus 1 over c subscript n close parentheses minus open parentheses fraction numerator begin display style m subscript 1 end style over denominator c subscript 1 end fraction plus fraction numerator begin display style m subscript 2 end style over denominator c subscript 2 end fraction... plus fraction numerator begin display style m subscript n end style over denominator c subscript n end fraction close parentheses
T a k e space 1 over c subscript 1 plus 1 over c subscript 2 plus.... plus 1 over c subscript n equals A space a n d space fraction numerator begin display style m subscript 1 end style over denominator c subscript 1 end fraction plus fraction numerator begin display style m subscript 2 end style over denominator c subscript 2 end fraction... plus fraction numerator begin display style m subscript n end style over denominator c subscript n end fraction equals B
rightwards double arrow n over h equals k over h A minus B
rightwards double arrow n equals k A minus h B
H e n c e comma space t h e space l o c u s space o f space R space i s space B X minus A y plus n equals 0 space w h i c h space i s space a space s t r a i g h t space l i n e
Answered by Renu Varma | 19 Sep, 2019, 10:53: AM
JEE main - Maths
Asked by virajpawar7701 | 26 May, 2024, 09:59: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
Asked by kantarathi293 | 04 May, 2024, 11:16: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
Asked by thanusri2 | 11 Mar, 2024, 19:39: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
Asked by umbarkarakash7 | 14 Jan, 2023, 10:57: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
Asked by sanjaysingh.srct | 05 Sep, 2019, 12:46: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
Asked by Surjitsp6u | 03 Sep, 2019, 22:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
Asked by Surjitsp6u | 26 Aug, 2019, 23:52: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT