...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...

...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...

...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...

...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...

...may be stated as follows : For the modular method, " 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 faced plane, is a surface of the second degree." The fixed point...

...Thus we see that the ellipse is 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). The distance from the focus is less than that from the directrix. FOCI OF CONICS....

...Definitions. A Conic Section, or Conic, is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line. The fixed point is called a focus, the fixed straight line is called a directrix, and...

...get the following theorem : — 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 having double contact with the circle; the contact will be real when the line L cuts S ; imaginary...

...rectangular axes or as the locus of a point which- moves so that its distance from a fixed point (F) is in a constant ratio to its distance from a fixed line (JOT), ie the two definitions of the ellipse already given are really identical. From the symmetry...