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Libros Libros 81 a 90 de 126 sobre To prove that the locus of the middle points of a system of parallel chords of a...
" To prove that the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis of the parabola. "
A Treatise on Infinitesimal Calculus: The dynamics of material systems. 1862 - Página 13
1862
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Exercises in Geometry

Grace Lawrence Edgett - 1909 - 81 páginas
...equilateral triangle, a circle, and a square are each 198, find the area of each figure. LOCI THEOREMS 1. The locus of the middle points of a system of parallel chords is a diameter perpendicular to the chords. 2. If two circles are tangent externally, their common internal...
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A Course in Mathematics: Algebraic equations, functions of one variable ...

Frederick Shenstone Woods, Frederick Harold Bailey - 1907
...outside the limits of this work. 138. Definition and equation of a diameter. A diameter of a conic is the locus of the middle points of a system of parallel chords. Let Aa? + 2 Hxy + By*+ 2 Gx 0 (1) be any conic (fig. 140), ftS any chord which makes the angle 6 with...
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Analytic Geometry

Norman Colman Riggs - 1910 - 294 páginas
...the middle point of the chord, then a'2mc 62c 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 V— J ma2 This line is called a diameter of the...
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Analytic Geometry

Norman Colman Riggs - 1910 - 294 páginas
...lines are called conjugate diameters. 16. Prove that in the hyperbola — — — = 1 the equation of the locus of the middle points of a system of parallel chords of slope »» is 17. Through the point (z0, Jto) on the ellipse 62x2 + а2у2 = а362 a diameter is...
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Analytic geometry

Norman Colman Riggs - 1911 - 294 páginas
...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...
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Brief Course in Analytic Geometry

John Henry Tanner, Joseph Allen - 1911 - 282 páginas
...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...
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Reinforced Concrete Construction ...: Prepared in the Extension ..., Volumen 3

George A. Hool - 1916
...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...
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New Analytic Geometry

Percey Franklyn Smith, Arthur Sullivan Gale - 1912 - 342 páginas
...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...
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Analytic Geometry

Linnaeus Wayland Dowling, Frederick Eugene Turneaure - 1914 - 266 páginas
...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...
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Analytic Geometry

Wallace Alvin Wilson, Joshua Irving Tracey - 1915 - 212 páginas
...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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