Show that the locus of a point such that the ratio of its distances from two given points is constant, is a circle. Hence show that the circle cannot pass through the given points.

The locus of a point which moves such that its distance from a given point is constant is

The locus of a point which moves so that the difference of the squares of its distances from two given points is constant, is a

The locus of a point which moves so that the difference of the squares of its distance from two given points is constant, is a

The locus of the point which moves such that the ratio of its distance from two fixed point in the plane is always a constant k(< 1) is

The locus of the point equidistant from two given points a and b is given by

Prove that the locus of a point which moves such that the sum of the square of its distances from the vertices of a triangle is constant is a circle having centre at the centroid of the triangle.

The equation of the circle passing through the point (1,1)

Show that the locus of the point, the powers of which with respect to two given circles are equal, is a staight line.