...= - CF. Hence, a circular cubic of the fourth class may be considered as the locus of a point whose distance from a fixed point is equal to its distance from a fixed circle, the latter distance being measured on the radius vector to a fixed point of the circle. This...

...the definitions, and investigate some of their properties from their equations. DBF. A conic section is the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line. If this ratio be unity, the curve...

...ellipse, an hyperbola, a circle, two straight lines, one straight line, or a point. Hence the term come section is applied to the parabola, ellipse, and hyperbola...equal to its distance from a fixed straight line. X Let 8 be the fixed point, YY' the fixed straight line. Draw SO perpendicular to YY'; take 0 as the...

...normals at the ends of the latera recta. 16. Find the equation to the hyperbola, considering it as the locus of a point which moves, so that its distance from one fixed point differs by a constant quantity from its distance from another fixed point. Show that...

...the line joining the other two. (Ex. 29, Chap, vi.) CHAPTER VIII. THE PARABOLA. 103, A conic section is the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line. The conic section is a parabola,...

...Parabola may be defined by the following property: The distance of the variable point of the curve from a fixed point is equal to its distance from a fixed right line. iy We may therefore trace the curve and find its figure as follows : — Take any point...

...meet ; find the locus of its centre. CHAPTER VI. THE ELLIPSE. 43. !• IF we define a conic section as "the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line" (Todhunter, Art. 123), we shall...

...extended to include the circle, two straight lines, one straight line and point. We shall also shew that every curve of the second degree must be a conic...which moves so that its distance from a fixed point is egual to its distance from a fixed straight line. Let 8 be the fixed point, YY the fixed straight line....

...both in simplicity and in the importance of its applications, is the parabola. It may be defined as The locus of a point which moves so that its distance from a fixed point is equal tu its distance from a fixed straight line. The fixed point (F in figure) is called the focus of the...

...O'Brien's Co-ordinate Geometry, p, I Fig. 50, 52. A Parabola is the locus of a point moving in a plane so that its distance from a fixed point is equal to its distance from a fixed right line. The fixed point is called the Focus ; the fixed right line is called the Directrix ; the...