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

If the area (in sq. units) of the triangle formed by the intersection of a line parallel to the x - axis and passing through the point P(h, k) with the line y=x and x+y=2 is 4h^(2) , then the locus of the point P is

A point P(x,y,z) is such that 3PA=2PB where AandB are the point (1,3,4) and (1,-2,-1), irrespectivley. Find the equation to the locus of the point P and verify that the locus is a sphere.

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 .

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P(h,k) with the lines y=x and x+y=2 is 4h^(2). Find the locus of the point P.

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

Let P be a variable point on the parabola y = 4x ^(2) +1. Then, the locus of the mid- point of the point P and the foot of the perpendicular drawn from the point P to the line y =x is:

If two tangents drawn from a point P to the parabola y^(2)=16 (x-3) are at right angles, then the locus of point P is :

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P(h,k) with the lines y=x and x+y=2is4h2. Find the locus of the point P

Perpendicular tangents are drawn from an external point P to the parabola y^2=16(x-3) Then the locus of point P is