Let A and A' be the points (5,0) and (-5,0) respectively. Find the equation of the locus of all points P(x,y) such that |AP| - |A'P| = 8.

A and A’ be the points (5, 0) and (-5, 0) respectively. Find the equation of the set of all points P(x, y) such that | AP |-1 A’P | = 6.

Find the equation of the locus of the points twice as from (-a, 0) as from (a, 0).

Two charges of +2xx10^-8C and -10^-8C are placed at points A and B respectively. Find the resultant force on a charge of 1 muC held at point P, such that AP = 10 cm, BP = 5cm angle angleAPB = 90^@

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is

Find the equation of the locus of all points, the sum of whose distances from (3, 0) and (9, 0) is 12.

A variable line L drawn through O(0,0) to meet line l1: y-x-10=0 and L2:y-x-20=0 at the point A and B respectively then locus of point p is ' such that (OP)^(2) = OA . OB,

The angle between a pair of tangents from a point P to the circle x^2 + y^2 = 25 is pi/3 . Find the equation of the locus of the point P.

Find the Sum of 5th term of A.P if a=1 , d=2

For a point P in the plane, let d_(1)(P) " and " d_(2)(P) be the distance of the point P from the lines x-y=0 and x+y=0, respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 le d_(1)(P) +d_(2)(P) le 4, is_____.