Home
Class 12
MATHS
A variable line passing through the orig...

A variable line passing through the origin intersects two given straight lines `2x + y = 4 and x + 3y = 6` at R and S respectively. A point P is taken on this variable line. Find the equation to the locus of the point P if (a) OP is the arithmetic mean of OR and OS. (b) OP is the geometric mean of OR and OS. (c) OP is an harmonic mean of OR and OS

Promotional Banner

Similar Questions

Explore conceptually related problems

A straight line through the origin 'O' meets the parallel lines 4x+2y=9 and 2x+y=-6 at points P and Q respectively.Then the point 'divides the segment PQ in the ratio

A variable line L is drawn through O(0, 0) to meet lines L1: 2x + 3y = 5 and L2: 2x + 3y = 10 at point P and Q, respectively. A point R is taken on L such that 2OP.OQ = OR.OP + OR.OQ. Locus of R is

Find the equation of a line passing through the point of intersection of the lines 2x-7y+11=0 and x+3y=8 and passes through the point (2,-3) .

A line passing through the origin O(0,0) intersects two concentric circles of radii a and b at P andQ,If the lines parallel to the X-and Y-axes through Q and P ,respectively, meet at point R, then find the locus of R.

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

Two straight lines passing through the point A(3, 2) cut the line 2y=x+3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ is

A variable line is drawn through O to cut two fixed straight lines L_(1) and L_(2) in R and S.A point P is chosen the variable line such (m+n)/(OP)=(m)/(OR)+(n)/(OS) Find the locus of P which is a straight ine passing through the point of intersection of L_(1) and L_(2)

Find the equation of a line passing through the point of intersection of the lines x+y=4 and 2x-3y-1=0 and parallel to a line whose intercepts on the axes are 4 and 6 units.