If P be a point on the lane `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`.

If P is any point on the plane lx+my+nz=p and Q is a point on the line OP such that OP.OQ=p^(2), then find the locus of the point Q.

If P be any point on the plane ln+my+nz=P and Q be a point on the line OP such that (OP)(OQ)=P^(2). The locus of point Q is

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

if P,Q are two points on the line 3x+4y+15=0 such that OP=OQ=9 then the area of triangle OPQ is

A straight line is drawn from a fixed point O meeting a fixed straight line in P . A point Q is taken on the line OP such that OP.OQ is constant. Show that the locus of Q is a circle.

Let P be a point on x^2 = 4y . The segment joining A (0,-1) and P is divided by point Q in the ratio 1:2, then locus of point Q is

A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to the line y = x. If the parameters of the points P & Q on the parabola are p & q respectively, show that p + q = 2. Also show that the locus of the point of intersection of the normals at P & Q is 2x - y = 12.

If P and Q are two points on the line 3x + 4y = - 15, such that OP = OQ = 9 units, the area of the triangle POQ will be