`O A` and `O B` are fixed straight lines, `P` is any point and `P M` and `P N` are the perpendiculars from `P` on `O Aa n dO B ,` respectively. Find the locus of `P` if the quadrilateral `O M P N` is of constant area.

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

A straight line is drawn through P(3,4) to meet the axis of x and y at Aa n dB , respectively. If the rectangle O A C B is completed, then find the locus of Cdot

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 PdotO Q=p^2 , then find the locus of the point Qdot

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 PdotO Q=p^2 , then find the locus of the point Qdot

O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is (a)4:1 (b) 2:1 (c) 8:3 (d) 7:3

From a point, P perpendicular PM and PN are drawn to x and y axes, respectively. If MN passes through fixed point (a,b), then locus of P is

A straight line passes through a fixed point (6,8) : Find the locus of the foot of the perpendicular drawn to it from the origin O.

A variable line through the point P(2,1) meets the axes at Aa n dB . Find the locus of the centroid of triangle O A B (where O is the origin).

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a) 2 (b) 2/3 (c) 1/3 (d) 3

A line O P through origin O is inclined at 30^0a n d45^0toO Xa n dO Y , respectivley. Then find the angle at which it is inclined to O Zdot