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 points P moves such that its distances from (1,2) and (-2,3) are equal.Then,the locus of P is

A point P moves such that its distances from two given points A and B are equal. Then what is the locus of the point P ?

Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (-5, 0). If the locus of the point P is a circle of radius r, then 4r^2 is equal to _______ .

A fixed point is at a perpendicular distance a from a fixed straight line and a point moves so that its distance from the fixed point is always equal to its distance from the fixed line.Find the equation to its locus,the axes of coordinates being drawn through the fixed point and being parallel and perpendicular to the given line.

A(0,1) and B(0,-1) are 2 points.If a variable point P moves such that sum o its distance from A and B ia 4 Then the locus of P is the equation of the form of (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 find the value of a^(2)+b^(2)

P is a point on the line x=y. If the distance of P from (1,3) is 10 then x and y coordinates of P are both equal to