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`

A point P is taken on 'L' such that 2/(OP) = 1/(OA) +1/(OB) , then the locus of P is

Let O be the vertex and Q be any point on the parabola, x^2=""8y . It the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

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 normal at a point P, on the ellipse x^2+4y^2=16 meets the x-axis at Q. If M is the mid-point of the line segment PQ, then the locus of M intersects the latus-rectum of the given ellipse at the points :

The angle between a pair of tangents from a point P to the circle x^2 + y^2 = 25 is pi/3 . Find the equation of the locus of the point P.

The tangent to the curve y=x-x^(3) at a point p meets the curve again at Q. Prove that one point of trisection of PQ lies on the Y-axis. Find the locus of the other points of trisection.

Find a point P on the line 3x+2y+10=0 such that |PA - PB| is minimum where A is (4,2) and B is (2,4)

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

Let P be a point on the circle x^(2)+y^(2)=9 , Q a point on the line 7x+y+3=0 , and the perpendicular bisector of PQ be the line x-y+1=0 . Then the coordinates of P are