 | Sir Gooroodass Banerjee - Education - 1910 - 380 pages
...of rotation of a line about a point, into the definition of an angle, and "regards the diameter as the locus of the .middle points of a system of parallel chords, and the tangent as the limiting position of a secant. • It will thus be seen that Euclid's method,... | |
 | Norman Colman Riggs - Geometry, Analytic - 1911 - 330 pages
...yi) is the middle point of the chord, then a'2mc We 14. From the preceding example, by eliminating c, prove that the locus of the middle points of a system of parallel chords, with slope m, of the ellipse is the straight line 62 y- — ,xma2 This line is called a diameter of... | |
 | John Henry Tanner, Joseph Allen - Geometry, Analytic - 1911 - 328 pages
...major auxiliary circle. 122. Diameters. As already shown in Art. 108, the definition of a diameter as the locus of the middle points of a system of parallel chords leads directly to its equation, for the ellipse : viz., Eq. [52] 62 y = - -T- *• a2m The form of... | |
 | University of Calcutta - 1911 - 760 pages
...of ;/=sin x; and write down tin- general 10 value of the angle, the sine of which ia J. GBOUP C. 1. The locus of the middle points of a .system of parallel chords 10 of a parabola is a straight line parallel to the axis of the parabola. Show that this line meets... | |
 | University of Calcutta - 1912 - 746 pages
...configuration of a constant cross-ratio. 2. Assuming a focus to be an intersection of two isotropic tangents, prove that the locus of the middle points of a system of parallel chords of a conic is a straight line meeting the directrix on the straight line through the focus perpendicular... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1912 - 364 pages
...somewhat different class of locus problems is illustrated in the following example. EXAMPLE What is the locus of the middle points of a system of parallel chords of an ellipse ? Solution. Let the equation of the system of parallel chords be (0) y = mx + k, where fc... | |
 | George A. Hool - Concrete - 1916 - 728 pages
...from the center. A diameter is any straight line passing through the center of the ellipse, and is the locus of the middle points of a system of parallel chords. (See Fig. 36C.) The major and minor axes of an ellipse are the only diameters perpendicular to the... | |
 | Newfoundland Council of Higher Education - 1912 - 300 pages
...of a circle bisect a chord which does not pass through the centre, it cuts it at right angles. Find the locus of the middle points of a system of parallel chords drawn in a circle. (14) C 8. Show how to draw a circle which shall pass through two given points and'have... | |
 | Linnaeus Wayland Dowling, Frederick Eugene Turneaure - Geometry, Analytic - 1914 - 294 pages
...properties 120 DIAMETERS 101. Definition of diameter 123 102. Conjugate diameters ......... 123 103. The locus of the middle points of a system of parallel chords . 125 POLES AND POLAR LINES 104. Definition of pole and polar line 127 105. Geometric properties of... | |
 | Wallace Alvin Wilson, Joshua Irving Tracey - Geometry, Analytic - 1915 - 236 pages
...equal. Exercise 6. Show how to draw a tangent to an ellipse at any point. 143. Diameters of a Conic. — The locus of the middle points of a system of parallel chords of any conic is called a diameter of the conic. Let a chord with slope ui meet the ellipse in the points... | |
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The locus of the middle points of a system of parallel chords in a parabola is called a diameter. 
