| Rufus B. Howland - 1887 - 60 páginas
...since m falls on both the ellipse and the line On, it will fall at n, aud Om = On - OP. THEOREM XIII. **The sum of the distances from any point on the ellipse to the** two foci is constant and equal to the major axis. Take P any point on the ellipse ; we are to prove... | |
| Albert Luther Candy - 1904 - 248 páginas
...the line through the foci as the ж-axis, and the point midway between the foci as origin. Let 2 a = **the sum of the distances from any point on the ellipse to the foci.** Let F(c, 0) and F'(— c, 0) be the two foci. Let P(x, y) be any point on the locus. Then FP + F'P... | |
| 1912
...points of which are so located with respect to two points within the curved line, called the foci, **that the sum of the distances from any point on the ellipse to the foci is** constant or equal for any one ellipse. Referring to the figure, the combined length of the two lines... | |
| Alexandre Koyré - 1992 - 530 páginas
...(point of intersection of the major and minor axes), which points it is his custom to call 'foci'93; and **the sum of the distances from any point on the ellipse to** these foci is always equal to the major axis. It follows that the distance from the points of the ellipse... | |
| Marcia Lerner - 1997 - 246 páginas
...foci and the distance from the origin to b. You already know these distances as b and c, and you know **that the sum of the distances from any point on the ellipse to the foci is** 2fl. The point (0, b) on the y-axis is halfway between the foci, and the sum of its distances from... | |
| Carlos I. Calle - 2001 - 647 páginas
...ellipse (figure 6.10). The position of each tack is called a focus. Since the string is not elastic, **the sum of the distances from any point on the ellipse to the** two foci is always the same. Kepler placed the Sun at a focus of the ellipse. His calculations showed... | |
| Stephen Fletcher Hewson - 2003 - 526 páginas
...focus of the ellipse3. 3For the ellipse (j/a)2 + (y/b)2 = 1 the foci are the points (±\/a2 - 62,0). **The sum of the distances from any point on the ellipse to the** two foci is a constant. Different values of e giving different shapes of ellipse, with the special... | |
| Steven A. Leduc, Princeton Review - 2004 - 645 páginas
...from X to the center of the earth is equal to the semimajor axis, a = ^(r} + r2). (This is because **the sum of the distances from any point on the ellipse to the** two foci must equal 2a = rl + r2, and X is equidistant from the two foci, one of which is at the center... | |
| Arjun Tan - 2008 - 281 páginas
...L. From symmetry, we have [cf. Stein (1977)] LL I rds= f r'ds. (3.100) oo By virtue of the property **that the sum of the distances from any point on the ellipse to the** two foci is constant and equal to the major axis, we get L r LL -| LL frds=- frds+fr'ds = - f (r +... | |
| 1997
...J. We know that BBl , the minor axis, is a line of symmetry in the ellipse; so: BF=BF1. We also know **that the sum of the distances from any point on the ellipse to the** two foci is always the same. The A sum of the distances from B is BF+BF1; from A it is AF+AFl. So:... | |
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