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 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.

P is a point on the line y+2x=1, and Qa n dR two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is

Two points P(a,0) and Q(-a,0) are given. R is a variable point on one side of the line P Q such that /_R P Q-/_R Q P is a positive constant 2alphadot Find the locus of the point Rdot

Let O be the vertex and Q be any point on the parabola x^(2) = 8 y . If the point P divides the line segments 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

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

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

The tangent at any point P on the circle x^(2)+y^(2)=2 , cuts the axes at L and M. Find the equation of the locus of the midpoint L.M.