Let `l_1` be the line in xy-plane with x and y intercepts `1/8` and `1/(4sqrt2)` respectively, and `l_2` be the line in zx-plane with x and z intercepts `-1/8 and -1/(6sqrt3)` respectively . If d is the shortest distance between the line `l_1 and l_2`, then `d^(-2)` is equal to

The shortest distance between the two lines L_1:x=k_1, y=k_2 and L_2: x=k_3, y=k_4 is equal to

Let L denote the line in the x - y plane with x and y intercepts as 3 and 1 respectively . The the image of the point (-1,-4) in this line is :

Find the shortest distance between the lines l_(1) and l_(2) given by (x-1)/-1=y/3=(z-2)/2 and x/2 =(y-1)/-6=z/-4

Two lines L_(1) and L_(2) of slops 1 are tangents to y^(2)=4x and x^(2)+2y6(2)=4 respectively, such that the distance d units between L_(1) and L _(2) is minimum, then the value of d is equal to

Let a line L_(1):3x+2y-6=0 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 R and S respectively.The locus of point of intersection of the lines PS and QR is

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)

The length of the chord intercepted on the line 2x-y+2=0 by the parabola x^(2)=8y is l then l=

Let L_1 and L_2 be the lines whose equation are (x-3)/3=(y-8)/-1=(z-3)/1 and (x+3)/--3=(y+7)/2=(z-6)/4 and respectively. A and B are two points on L_1 and L_2 respectively such that AB is perpendicular both the lines L_1 and L_2. Find points A, B and hence find shortest distance between lines L_1 and L_2

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