Home
Class 12
MATHS
Let L1=0a n dL2=0 be two fixed lines. A ...

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`

Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise The Straight Lines Exercise 7 : (Subjective Type Questions)|4 Videos

  • 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 (Statement I And Ii 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

Find the equation of the line passing through the points (1,2,3)a n d(-1,0,4)dot

Find the equation of the straight lines passing through the following pair of point: (0,0)a n d\ (2,-2)dot

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 .

A straight line is drawn from a fixed point O meeting a fixed straight line in P . A point Q is taken on the line OP such that OP.OQ is constant. Show that the locus of Q is a circle.

Find the equation of the straight line through the point (alpha,beta) and perpendiculasr to the line l x+m y+n=0.

The locus of the centre of the circle passing through the origin O and the points of intersection A and B of any line through (a, b) and the coordinate axes is

A straight lien is drawn from a fixed point O metting a fixed straight line P . A point Q is taken on the line OP such that OP.OQ is constant. Show that the locus of Q is a circle.

A variable line cuts n given concurrent straight lines at A_1,A_2...A_n such that sum_(i=1)^n 1/(OA_i) is a constant. Show that it always passes through a fixed point, O being the point of intersection of the lines

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O P.O Q=p^2 , then find the locus of the point Qdot

A variable line through the point P(2,1) meets the axes at A an d B . Find the locus of the centroid of triangle O A B (where O is the origin).