 | George Cunningham Edwards - Geometry - 1895 - 330 pages
...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.... | |
 | Frederick Harold Bailey - Geometry, Analytic - 1897 - 392 pages
...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)... | |
 | Frederick Shenstone Woods, Frederick Harold Bailey - Mathematics - 1907 - 424 pages
...are on the same straight line (§ 29, 5) and cannot determine a circle. 73. The ellipse. An ellipse is the locus of a point the sum of the distances of which from two fixed points is constant. The two fixed points are called the foci. Let them be denoted by F and F' (fig. 82) and let the axis... | |
 | Charles Sumner Slichter - Functions - 1914 - 516 pages
...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... | |
 | Charles Sumner Slichter - Functions - 1914 - 520 pages
...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... | |
 | Frederick Shenstone Woods, Frederick Harold Bailey - Calculus - 1917 - 542 pages
...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 sum of the distances of which from two 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... | |
 | Frederick Shenstone Woods, Frederick Harold Bailey - Calculus - 1917 - 536 pages
...of the two circles and 40z2 + 40/-400^ + 5202/ + 2429 = 0 CEETAIN CURVES 38. The ellipse. An ellipse is the locus of a point the sum of the distances of which from two fixed point's is constant. The two fixed points are called the foci. Let them be denoted by F and F' (fig.... | |
 | Frederick Shenstone Woods - 1917 - 562 pages
...— ^-, r = — — — Hence each of the two circles and CERTAIN CURVES 38. The ellipse. An ellipse is the locus of a point the sum of the distances of yihich from two fixed points is ccnstant. The two fixed points are called the/oei. Let them be denoted... | |
 | Tobias Dantzig, Joseph Mazur - Mathematics - 2007 - 420 pages
...which had some measurable position with respect to some fixed reference system. Thus the ellipse was the locus of a point the sum of the distances of which from two fixed points was constant. Such a description was in fact a rhetorical equation of the curve, for it furnished the... | |
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Let them be denoted by F and F' (fig. 72), and let the axis of x be taken through them, and the origin halfway between them. Then if P is any point on the ellipse and 2 a represents the constant sum of its distances from the foci, we have F'P+FP=2a. 