The coordinates of the point `Aa n dB` are (a,0) and `(-a ,0),` respectively. If a point `P` moves so that `P A^2-P B^2=2k^2,` when `k` is constant, then find the equation to the locus of the point `Pdot`

Co-ordinates of points P and Q are -2 and 2 respectively. Find d(P,Q).

If A and B be the points (3,4,5) and (-1,3,-7) , respectively, find the equation of the set of points P such that PA^(2)+PB^(2)=k^(2) , where k is a constant.

If P(2,-7) is a given point and Q is a point on (2x^(2)+9y^(2)=18) , then find the equations of the locus of the mid-point of PQ.

Two points P(a,0) and Q(-a,0) are given. R is a variable point on one side of the line P Q such that /_R P Q-/_R Q P is a positive constant 2alphadot Find the locus of the point Rdot

A B is a variable line sliding between the coordinate axes in such a way that A lies on the x-axis and B lies on the y-axis. If P is a variable point on A B such that P A=b ,P b=a , and A B=a+b , find the equation of the locus of Pdot

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

Tangents P Aa n dP B are drawn to x^2+y^2=a^2 from the point P(x_1, y_1)dot Then find the equation of the circumcircle of triangle P A Bdot

If the points P(6,2) and Q(-2,1) and R are the vertices of a DeltaPQR and R is the point on the locus of y=x^(2)-3x+4 , then find the equation of the locus of centroid of DeltaPQR .