Let a given line `L_1` intersect the X and Y axes at P and Q respectively. Let another line `L_2` perpendicular to `L_1` cut the X and Y-axes at Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

A given line L_1 cut x and y-axes at P and Q respectively and has intercepts a and b/2 on x and y-axes respectively. Let another line L_2 perpendicular to L_1 cut x and y-axes at R and S respectively. Let T be the point of intersection of PS and QR . A straight line passes through the centre of locus of T . Then locus of the foot of perpendicular to it from origin is : (A) a straight line (B) a circle (C) a parabola (D) none of these

A given line L_1 cut x and y-axes at P and Q respectively and has intercepts a and b/2 on x and y-axes respectively. Let another line L_2 perpendicular to L_1 cut x and y-axes at R and S respectively. Let T be the point of intersection of PS and QR . Locus of T is a circle having centre at (A) (a, b) (B) (a, b/2) (C) (a/2, b) (D) (a/2, b/4)

A given line L_1 cut x and y-axes at P and Q respectively and has intercepts a and b/2 on x and y-axes respectively. Let another line L_2 perpendicular to L_1 cut x and y-axes at R and S respectively. Let T be the point of intersection of PS and QR . If two chords each bisected by x-axis can be drawn from (a, b/2) to the locus of T , then (A) a^2 gt 2b^2 (B) b^2 gt 2a^2 (C) a^2 lt 2b^2 (D) b^2 lt 2a^2

The line x+y=1 cuts the coordinate axes at P and Q and a line perpendicular to it meet the axes R and S. The equation to the locus of the intersection of lines PS and QR is

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these

The equation of the straight line through the intersection of line 2x+y=1 and 3x+2y=5 passing through the origin, is:

The straight line x/a+y/b=1 cuts the axes in A and B and a line perpendicular to AB cuts the axes in P and Q. Find the locus of the point of intersection of AQ and BP .

Let a line x/a+y/b=1 intersects the x-axis at A and y-axis at B resapectively. A line parallel to it is drawn to intersect the axes in P and Q respectively. The extermities of the lines are joined transversely. If the locus of point of intersection of the line joining them is x/a=cy/b, then c is equal to

Show that the four points of intersection of the lines : (2x-y + 1) (x-2y+3) = 0 , with the axes lie on a circle and find its centre.