If P be a point on the plane `lx+my+nz=p and Q` be a point on the OP such that OP. OQ=p^2 show that the locus of the point Q is `p(lx+my+nz)=x^2+y^2+z^2`.

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, q, r) be a point on the plane 2x+2y+z=6 , then the least value of p^2+q^2+r^2 is equal ot

If P N is the perpendicular from a point on a rectangular hyperbola x y=c^2 to its asymptotes, then find the locus of the midpoint of P N

If the line lx + my = 1 is a tangent to the circle x^(2) + y^(2) = a^(2) , then the point (l,m) lies on a circle.

A(-2, 2, 3) and B(13, -3, 13) and L is a line through A. Q. A point P moves in the space such that 3PA=2PB , then the locus of P is

Show that the relation R in the set A of points in a plane give by R = {(P,Q) : distance of the point P from the origin is same as the distance of the point Q from the origin} , is an equivalence relation. Further , show that the set equivalence relation . Further , show that the set of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.

The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.

If P(x, y) is a point equidistant from the points A(6, -1) and B(2, 3), show that x-y = 3.

Find the image of the point P (3, 5, 7) in the plane 2x + y + z=0 .

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :