Find a point P on the line `3x+2y+10=0` such that `|PA - PB| `is minimum where A is (4,2) and B is (2,4)

The locus of the moving point P such that 2PA=3PB , where A is (0,0) and B is (4,-3), is

Find the points on the line x+y=4 which lie at a unit distance from the line 4x+ 3y=10 .

Determine the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A(2,-2) and B(3,7).

Find the equation of set of points P such that PA^(2)+PB^(2)=2k^(2) , where A and B are the points (3, 4, 5) and (-1,3,-7) , respectively.

Let the curve C be the mirror image of the parabola y^2 = 4x with respect to the line x+y+4=0 . If A and B are the points of intersection of C with the line y=-5 , then the distance between A and B is

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Find points on line x + y + 3 = 0 whose distance from line x+2y+2=0 is sqrt(5) unit.

The line segment joining the points P(3,3) and Q(6,-6) is trisected by the points A and B such that A is nearer to p. If A also lies on the line given by 2x + y + k = 0 , find the value of k.