Home
Class 12
MATHS
Given n sraight lines and a fixed point ...

Given n sraight lines and a fixed point O.A straight line is drawn through O meeting these lines in the points `R_(1),R_(2),R_(3),……R_(n)` and a point R is taken on it such that
` n/(OR)= sum_(r=1)^(n) 1/(OR_(r))` ,
Prove that the locus of R is a straight line .

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THE STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|17 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Subjective Type Questions)|8 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

Similar Questions

Explore conceptually related problems

Let L_1=0a n dL_2=0 be two fixed lines. A variable line is drawn through the origin to cut the two lines at R and SdotPdot is a point on the line A B such that ((m+n))/(O P)=m/(O R)+n/(O S)dot Show that the locus of P is a straight line passing through the point of intersection of the given lines R , S , R are on the same side of O)dot

sum_(r=1)^n r (n-r +1) is equal to :

Knowledge Check

  • If R is a relation on the set of all straight lines drawn in a plane defined by l_(1) R l_(2) iff l_(1)botl_(2) , then R is

    A
    reflexive
    B
    symmetric
    C
    transitive
    D
    an equivalence relation

    • Similar Questions

    Explore conceptually related problems

    sum_(r=1)^n r(n-r) is equal to :

    If S_(n) = sum_(r=1)^(n) (r )/(1.3.5.7"……"(2r+1)) , then

    (sum_(r=1)^n r^4)/(sum_(r=1)^n r^2) is equal to

    Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

    If f(n)=sum_(r=1)^(n) r^(4) , then the value of sum_(r=1)^(n) r(n-r)^(3) is equal to

    sum_(r=1)^(n) (-1)^(r-1) ""^nC_r(a - r) =

    The value of sum_(r=1)^(n)(""^(n)P_(r))/(r!) is

    Home
    Profile