...S is a circle. We learn that the locus of a point, such that the tangent from it to a fixed circle is in a constant ratio to its distance from a fixed line, is a conic touching the circle at the two points where the fixed line meets it; or, conversely, that if...

...MN. CHAPTER XI. THE HYPERBOLA. 209. To find the equation to the hyperbola. The hyperbola 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 ratio being greater than unity....

...conic section may be defined as the locus of a point whose distance from a fixed point (the focus) is in a constant ratio to its distance from a fixed line (the directrix). On this definition several writers have based the theory of conic sections. Taking...

...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...

...published in the third volume of the Cambridge and Dublin Mathematical Journal. The locus of a point whose distance from a fixed point is in a constant ratio to its distance from a fixed straight line, measured parallel to a fixed plane, is a surface of the second degree. Since this locus...

...the other two. (Ex. 29, Chap, vi.) CHAPTER VIII. THE PARABOLA. f 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,...

...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,...

...mentioned above, that the Conic may be defined as the locus of a point whose distance from a jixed point is in a constant ratio to its distance from a fixed right line. In fact, this definition has been made the basis of several treatises upon the Conies....

...as before produced. 3. To produce the equation of the locus of a point moving so that the square of its distance from a fixed point is in a constant ratio to its distance from a fixed line. Sea's. — Let the fixed line be taken as the axis of abscissas, and let a perpendicular to it through...

...Defining a conic section to be the locus of a point whose distance from a fixed point called the focus is in a constant ratio to its distance from a fixed line, show that, if the constant ratio be less than unity, the curve consists of one closed oval whose points...