Given n straight line 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`. If R is the point on the line such that `n/(OR)=1/(OR_1)+1/(OR_2)+....+1/(OR_n)`, then show that the locus of R is a straight line.

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

The straight line 3x+y=9 divides the straight line segment joining the points (1, 3) and (2, 7) are in ratio

Find the equation of the straight line perpendicular to the line joining the points (2,3) and (3,-1) and passing through the points (2,1).

Two straight lines pass through the fixed points (+-a, 0) and have slopes whose products is pgt0 Show that the locus of the points of intersection of the lines is a hyperbola.

A straight line passes through (1,1) and portion of the line intercept between the axes is divided at this point in the ratio 3:4. Find the equation of the line.

The straight line through a fixed point (2,3) intersects the coordinate axes at distinct point P and Q. If O is the origin and the rectangle OPRQ is completed then the locus of R is

If the straight line joining the points (3,4) and (2,-1) be parallel to the line joining the points (a,-2) and (4,-a), find the value of a.

If the straight line joining the points A(3, 4, -1) and B(4, p, 2) is parallel to the straight line joining the points C(2, 1, q) and D(4, -3, 1), then -

If the straight line joining the points (4, -3, 2) and (3, -1, 5) is perpendicular to the straight line joining the points (m, -2, 1) and (7, 3, -2), then the value of m is -

Find the equation of the straight line equidistant from the point (2,-2) and the line 3x-4y+1=0.