If a point `P` moves such that its distance from `(a, 0)` is always equal to `a+x`-coordinate of `P`, show that the locus of `P` is `y^2 = 4ax`.

A point P moves so that its distance from the line given by x=-3 is equal to its distance from the point (3, 0). Show that the locus of P is y^(2)=12x .

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

A point moves such teat its distance from the point (4,0) is half that of its distance from the line x=16 , find its locus.

ABCD is a square with side AB = 2. A point P moves such that its distance from A equals its distance from the line BD. The locus of P meets the line AC at T_1 and the line through A parallel to BD at T_2 and T_3 . The area of the triangle T_1 T_2 T_3 is :

ABCD is a square with side AB = 2. A point P moves such that its distance from A equals its distance from the line BD. The locus of P meets the line AC at T_1 and the line through A parallel to BD at T_2 and T_3 . The area of the triangle T_1 T_2 T_3 is :

A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number (!=1) . Then, identify the locus of the point.

A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number (!=1) . Then, identify the locus of the point.

If the distances from P to the points ( 3, 4 ) , ( - 3, 4 ) are in the ratio 3 : 2, then the locus of P is

if P is a point on parabola y^2=4ax such that subtangents and subnormals at P are equal, then the coordinates of P are:

A point P is such that the sum of the squares of its distances from the two axes of co-ordinates is equal to the square of its distance from the line x-y=1 . Find the equation of the locus of P.