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`

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 the point (1,0) and Q is any point on the parabola y^(2) = 8x then the locus of mid - point of PQ is

If O is the origin and Q is a variable point on y^2=xdot Find the locus of the mid point of \ O Qdot

Let L_1=0a n dL_2=0 be two fixed lines. A variable line is drawn through the origin to cut the two lines at R and SdotPdot is a point on the line A B such that ((m+n))/(O P)=m/(O R)+n/(O S)dot Show that the locus of P is a straight line passing through the point of intersection of the given lines R , S , R are on the same side of O)dot

The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes in L and M . Find the locus of the middle point of LM .

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

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

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 :

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 :

T P and T Q are tangents to the parabola y^2=4a x at Pa n dQ , respectively. If the chord P Q passes through the fixed point (-a ,b), then find the locus of Tdot