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 straight lien is drawn from a fixed point O metting a fixed straight line 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 point Q is taken on this line such that OP.OQ is constant ,then locus of Q 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

Given n sraight lines and a fixed point O.A straight line is drawn through O meeting these lines in the points R_(1),R_(2),R_(3),……R_(n) and a point R is taken on it such that n/(OR)= sum_(r=1)^(n) 1/(OR_(r)) , Prove that the locus of R is a straight line .

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

Show that the locus of a point equidistant from a fixed point is a circle with the fixed point as centre.

if P,Q are two points on the line 3x+4y+15=0 such that OP=OQ=9 then the area of triangle OPQ is

A & B are two fixed points. The vertex C of △ABC moves such that cotA+cotB= constant. The locus of C is a straight line

Two circles intersect each other at points A and B. A straight line PAQ cuts the circles at P and Q. If the tangents at P and Q intersect at point T, show that the points P, B, Q and T are concylic.

A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.