O is a fixed point and P any point on a fixed circle , on OP is taken a point Q such that OQ is in a constant ratio to OP , prove that the locus of Q is circle

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

P is a variable point on a circle C and R is a fixed point on PQ dividing it in the ratio p:q where p>0 and q>0 are fixed.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.

Prove that the tangents from any point of a fixed circle of co-axial system to two other fixed circles of the system are in a constant ratio.

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.

A tangent is drawn from an external point O to a circle of radius 3 units at P such that OP = 4 units. If C is the centre of the circle, then the sine of the angle COP is

PR is a tangent at a point Q on a circle, in which Q is the centre and its radius is 8 cm. If OR = 16 cm and OP = 10 cm, then the length of PR 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 .