`Q` is a variable point whose locus is `2x+3y+4=0;` corresponding to a particular position of `Q ,P` is the point of section of `O Q ,O` being the origin, such that `O P: P Q=3: 1.` Find the locus of `Pdot`

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

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O P.O Q=p^2 , then find the locus of the point Qdot

Find the position vector of the mid point of the vector joining the points P(2,3,4) and Q(4,1,-2).

Let P be a point on the circle x^(2) + y^(2) = a^(2) whose ordinate is PN and Q is a point on PN such that PN : QN = 2 : 1 . Find the locus of Q and identify it

Let P be a point on the hyperbola x^2-y^2=a^2, where a is a parameter, such that P is nearest to the line y=2xdot Find the locus of Pdot

Let P be a variable point on a circle C and Q be a fixed point outside C. If R is the midpoint of the line segment PQ, then locus of R is

If tangents O Q and O R are dawn to variable circles having radius r and the center lying on the rectangular hyperbola x y=1 , then the locus of the circumcenter of triangle O Q R is (O being the origin). (a) x y=4 (b) x y=1/4 x y=1 (d) none of these

A variable straight line passes through the point of intersection of the staright lines x/a+y/b=1 and x/b+y/a=1 and intersects the axes at P and Q.Find the locus of mid-point of Pq.

If the coordinates of a variable point P are (acostheta,bsintheta), where theta is a variable quantity, then find the locus of Pdot

P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) is another variable point, where c is a constant. The locus of the midpoint of P Q is