A variable line through the point `((1)/5,1/5)`cuts the coordinate axes in the points A and B. If the point P divides AB internally in the ratio 3:1, then the locus of P is (A) `3x+y = 20xy` (B) `y + 3x = 20 xy` (C) `x + y = 20 xy` (D) `3x+3y = 20xy`

A variable line through the point (6/5, 6/5) cuts the coordinates axes in the point A and B . If the point P divides AB internally in the ratio 2:1 , show that the equation to the locus of P is : 5xy = 2( 2x+y) .

x + y = 5 xy , 3x + 2y = 13 xy ( x ne 0, y ne 0 )

If a variable line drawn through the intersection of the lines x/3+y/4=1 and x/4+y/3=1 meets the coordinate axes at A and B, (A !=B), then the locus of the midpoint of AB is (A) 6xy = 7 (x+y) (B) 4 (x+y)^2 - 28(x+y) + 49 =0 (C) 7xy = 6(x+y) (D) 14 (x+y)^2 - 97(x+y) + 168 = 0

A variable line through the point (p, q) cuts the x and y axes at A and B respectively. The lines through A and B parallel to y-axis and x-axis respectively meet at P . If the locus of P is 3x+2y-xy=0 , then (A) p=2, q=3 (B) p=3, q=2 (C) p=2, q=-3 (D) p=-3, q=-2

A variable line through the point (p, q) cuts the x and y axes at A and B respectively. The lines through A and B parallel to y-axis and x-axis respectively meet at P . If the locus of P is 3x+2y-xy=0 , then (A) p=2, q=3 (B) p=3, q=2 (C) p=2, q=-3 (D) p=-3, q=-2

Let a point P(h,k) satisfies the equation x^(3)+y^(3)+3xy=1 .Then the locus of the point P is

A straight line through the point A(-2, -3) cuts the line x+3y=9 and x+y+1=0 at B and C respectively. Find the equation of the line if AB.AC = 20 .

A variable straight line passes through the points of intersection of the lines x+2y=1 and 2x-y=1 and meets the co-ordinates axes in A and B. Prove that the locus of the midpoint Of AB is 10xy=x+3y.

The equation of the straight line which passes through the point (-4,3) such that the portion of the line between the axes is divided internally be the point in the ratio 5:3 is (A) 9x-20y+96=0 (B) 9x+20y=24 (C) 20x+9y+53=0 (D) None of these

The equation of the straight line which passes through the point (-4,3) such that the portion of the line between the axes is divided internally be the point in the ratio 5:3 is (A) 9x-20y+96=0 (B) 9x+20y=24 (C) 20x+9y+53=0 (D) None of these