The sum of the distance of a moving point from the points (4,0) and (-4, 0) is always 10 units . Find the equation of the locus of the moving point.

The sum of the distance of a moving point from the points (4,0) and (-4,0) is always 10 units. Find the equation to the locus of the moving point.

The ratio of the distances of a moving point from the points (3,4) and (1,-2) is 2:3 , find the locus of the moving point.

The sum of the squares of the distances of a moving point from two fixed points (a,0) and (-a ,0) is equal to a constant quantity 2c^2dot Find the equation to its locus.

Find the distance between the following pairs of points. (-4,0) and (3,0)

A point moves so that its distance from the point (2,0) is always (1)/(3) of its distances from the line y=x-18 . If the locus of the points is a conic, then length of its latus rectum is

If sum of the perpendicular distances of a variable point P(x, y) from the lines x+y-5= 0 and 3x - 2y +7=0 is always 10. Show that P must move on a line.

Find the distance of the point (3,-3) from the line 3x - 4y - 26 = 0

If the algebraic sum of the distances from the points (2,0), (0, 2) and (1, 1) to a variable line be zero then the line passes through the fixed point.

i. Find the coordinates of the point which trisect the line segment joining the points P(4,0,1) and Q(2,4,0) . (ii) Find the locus of the set of points P such that the distance from A(2,3,4) is equal to twice the distance from B(-2,1,2) .

A point moves such that the area of the triangle formed by it with the points (1,5) and (3,-7) is 21 sq. units. Then locus of the point is