...circle, having its centre in the line joining 0 to the centre of the circle on which P lies. 27. Prop. The locus of a point which moves in a plane so that its distances from two fixed points in that plane are in a constant ratio is a circle. B Let A and...

...of the tangent to C at the origin and of the line through the centres of the circles. 32. A point P moves in a plane so that the ratio of its distances from two fixed points A, B in the plane is constant. Prove that its locus is a circle. If PA/PB = A > 1,...

...of the pole of a normal chord of the parabola j/2 = 4аж. CHAPTEK X THE ELLIPSE 158. An ellipse is the locus of a point which moves in a plane so that its distance from a fixed point in the plane bears a constant ratio, which is less than unity, to its...

...specific points and lines lying in the plane containing the conic section. A conic section is defined as the locus of a point which moves in a plane so that its distance from a fixed point (called focus) is in a constant ratio (called eccentricity) to its...

...into two parts so that the chords of these parts may be to each other in a given ratio. 47. A point /' moves in a plane so that the ratio of its distances from two fixed points A, B in that plane is always the same. Show that in general the locus of P is a circle,...

...circle, having its centre in the line joining 0 to the centre of the circle on which P lies. 27. Prop. The locus of a point which moves in a plane so that its distances from two fixed points in that plane are in a constant ratio is a circle. Let A and B...