A straight line is drawn from a fixed point `O` meeting a fixed straight line in `P`. A point `Q` is taken on the line `OP` such that `OP.OQ` is constant. Show that the locus of `Q` is a circle.

A variable straight line is drawn from a fixed point O meeting a fixed circle in P and a point Q is taken on this line such that OP. OQ is constant, then locus of Q is : (A) a straight line (B) a circle (C) a parabola (D) none of these

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 straight line through a fixed point (2,3) intersects the coordinate axes at distinct point P and Q.If O is the origin and the rectangle OPRQ is completed then the locus of R is

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

A and B are two fixed points and the line segment AB always subtends an acute angle at a variable point P .Show that the locus of the point P is a circle.

If P be any point on the plane ln+my+nz=P and Q be a point on the line OP such that (OP)(OQ)=P^(2). The locus of point Q is

If P be a point on the lane lx+my+nz=p and Q be a point on the OP such that OP. OQ=p^2 show that the locus of the point Q is p(lx+my+nz)=x^2+y^2+z^2 .

A variable line is drawn through O to cut two fixed straight lines L_(1) and L_(2) in R and S.A point P is chosen the variable line such (m+n)/(OP)=(m)/(OR)+(n)/(OS) Find the locus of P which is a straight ine passing through the point of intersection of L_(1) and L_(2)

A straight line passes through a fixed point (2, 3).Locus of the foot of the perpendicular on it drawn from the origin is