...which A 77' the latus-rectum is , _ ,,- ." Again, take the ordinary definition .of an ellipse, that it is the locus of a point, the sum of the distances of which from two fixed points is constant. This is equivalent to " the sum of the distances from either focus, of the points of contact of two...

...simplest property of the hyperbola is that it is the locus of a point the difference of whose distances from two fixed points is constant. The two fixed points are called tho foci. This is analogous to the definition from which the properties and equation of the ellipse...

...and Fundamental Properties. 116. Def. An ellipse is the locus of a point the sum of whose distances from two fixed points is constant. The two fixed points are called foci of the ellipse. Thus, if the point P move in such a way that PF ' + PF' is constant, it will describe...

...straight lines. Remark. — Do not fail in each problem to discuss the particular cases. •* 82. Find the locus of a point, the sum of the distances of which from two vertices of an equilateral triangle equals its distance from the third vertex. N D FIG. 196. PROBLEMS....

...circle of which the centre is at the origin and the radius is 5. Again, let it be required to find the locus of a point, the sum of the distances of which from the points (— 1, 0) and (1, 0) is equal to 6. By [1], § 3, we have V(x + 1)' + y 2 + V(x — I)...

...second class (see CURVES ) , and may be defined as the locus of a point (P), the sum of whose distances from two fixed points is constant. The two fixed points are called the foci (F and F') ; the diameter drawn through them is called the major axis, and the perpendicular bisector...

...signs. By §77, such an equation represents an ellipse. Hence the ellipse might have been defined as the locus of a point, the sum of the distances of which from two fixed points is constant. An ellipse can be drawn by attaching a string of length 2a by pins at the points FI and ^"2 and tracing...

...signs. By §77, such an equation represents an ellipse. Hence the ellipse might have been defined as the locus of a point, the sum of the distances of which from tivo fixed points is constant. An ellipse can be drawn by attaching a string of length 2a by pins at...

...circles and 40 ж2 + 40 г/2 - 400 x + 520 у + 2429 = 0 satisfies the conditions of the problem. 38. The ellipse. An ellipse is the locus of a point the...fixed points is constant. The two fixed points are ealled the fon. Let them be denoted by F and F' (fig. 72), and let the axis of x be taken through them,...

...y2 - 48 x - 72 y - 936 = 0. 41. The hyperbola. An hyperbola is the locus of a point the. difference of the distances of which from two fixed points is...two fixed points are called the foci. Let them be F and F1 (fig. 74), and let FF1 be taken as the axis of a;, the origin being halfway between F and...