What is the locus of points, the difference of whose distances from two points being constant ?

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.

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.

Show that the locus of a point such that the ratio of its distances from two given points is a constant k(!=1) , is a circle.

Show that the locus of a point such that the ratio of its distances from two given points is a constant k (ne 1) is a circle.

Find the equation to the locus of a point whose difference of distances from the two fixed points (ae,0),(-ae,0) is constant and is equal to 2a where e>1.Hence identify the locus

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci