...So we must again resort to the language of co-ordinate geometry, and define a hyperbola as the locus of a point which moves so that its distance from a fixed point called a focus bears a constant ratio to its distance from a fixed straight line called the directrix,...

...The conic sections, or more briefly, conies, may be defined thus : A conic in a plane curve traced by a point which moves so that its distance from a fixed point bears always a constant ratio to its distance from a fixed straight line. The general equation of this...

...considering the mode of description and the equation of the hyperbola. The circle is a curve described by a point which moves so that its distance from a fixed point called the centre is constant. The hyperbola is a curve described by a point which moves so that the...

...ellipse should also be given. CHAPTER VI. THE HYPERBOLA : tfx2 oV = O262. 35. DEFINITION : The locus of a point which moves so that its distance from a fixed point i — 6 > 1 its distance from a fixed line (where e is a constant greater than 1), is called a hyperbola....

...radius drawn to the point of contact. CHAPTER TV. THE PARABOLA: y3 = 2px. 21. DEFINITION : The locus of a point which moves so that its distance from a fixed point its distance from a fixed line is cf.-lled a parabola. The fixed point is called the focus and the...

...radius drawn to the point of contact. CHAPTER IV. THE PARABOLA: y* = 2px. 21. DEFINITION: The locus of a point which moves so that its distance from a fixed point its distance from a fixed line is culled a parabola. = 1 The fixed point is called the focus and the...

...portions of the complete surface ; and in Art. 76 it was shown that the curve might be denned as the locus of a point which moves, so that its distance from a fixed point bears a constant ratio (greater than unity) to its distance from a fixed line. The curve is set out...

...curve." Let the latter be a parabola having the equation y=\ x. Now a parabola is denned as " the locus of a point which moves, so that its distance from a fixed point is in a constant relation to its distance from a fixed straight line." How do we construct such a curve ? yos FIG. 5....

...radius drawn to the point of contact. CHAPTER IV. THE PARABOLA: i/ 2 = 2px. 21. DEFINITION: The locus of a point which moves so that its distance from a fixed point its distance from a fixed line ~~ is called a parabola. The fixed point is called the focus and the...

...approaches as a limit the radical axis. CHAPTER IV THE PARABOLA 52. Conies. — TJie locus of a point tchich moves so that its distance from a fixed point is in...its distance from a fixed line is called a conic. f. The fixed point is called the focus and the fixed line the directrix. The line through the focus...