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Libros Libros 91 a 100 de 104 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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the encyclopedia americana

1919 The Encyclopedia Americana Corporation - 1919
...curve (2) r = . 1 — cos 9 Diameter of the Parabola. — A diameter of any curve is defined to be the locus of the middle points of a system of parallel chords. Let (:TI, yt) and (xt, y*) be the co-ordinates of P, and Pi, the extremities of the chord Pi P, (Fig....
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The Encyclopedia Americana: A Library of Universal Knowledge, Volumen 21

1919
...curve (2) r = — . 1 — cos 8 Diameter of the Parabola. — A diameter of any curve is defined to be the locus of the middle points of a system of parallel chords. Let (x,, y,) and (x,, y,) be the co-ordinates of P, and Pi, the extremities of the chord Pi P, (Fig....
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General Catalogue Issue

1876
...= 0. 3. To find the equation of that chord of a conic which is bisected at the origin ; and to show that the locus of the middle points of a system of parallel chords is a right line. 4. The general equation of the tangents to a conic from a point (x 1 y') being U 1 U =...
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A Course of Pure Geometry

...tangent at p is parallel to qq'. (2) (vt, pd) = -I, .'. tp=pv. (3) (vr, qq') = — 1, -'. q'v = vq. (4) The locus of the middle points of a system of parallel chords is a straight line meeting the curve in the point at infinity, that is, a straight line parallel to the...
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A Course of Pure Geometry

...diameter parallel to the chords is bisected at that point. In the case of the parabola, the line which is the locus of the middle points of a system of parallel chords is parallel to the axis. For such a system is the projection of chords of the circle concurrent at a point...
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A Textbook Of Mathematics

B.K. Dev Sarma - 2003 - 654 páginas
...y2 = 4ax at the point fi meets the curve again at the point rz, show that h - - h - 1lt\. 19. Prove that the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to its axis. 20. If V be variable parameter, find the vertex,...
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the methods of plane projective geometry based on the use of general ...

...triangle, when the conies are a system of coaxal circles which do not meet in real points. [MTI] 14. 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 curve. The tangents at two points P, Q...
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A Textbook Of Analytical Geometry Of Two Dimensions

Jain, P.K. - 1986 - 362 páginas
...parallel to the axis of the parabola is called a diameter of the parabola. As we have seen in § 7.2 that the locus of the middle points of a system of parallel chords to a parabola is a line parallel to the axis of the parabola, it is a diameter of the parabola. Thus...
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A Textbook Of Analytical Geometry Of Three Dimensions

P.K. Jain - 2005 - 376 páginas
..."*" ¿* ^ c2 а« ^ ¿2 r c2' 8.2 Locus of the middle points of a system of parallel chords. To find the locus of the middle points of a system of parallel chords of a conicoid. Let the equation of a conicoid be ax2 + by2 + cz2 = 1 (1) and let the chords be parallel...
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The Bombay University Calendar

University of Bombay - 1903
...point where the normal again meete the curve is my (1 + та*) + га2.* + a (2 + TO*)S = 0. 9. Find the locus of the middle points of a system of parallel chords of 10 an ellipse. The sides БС, CA of the triangle ABC are parallel to the diameters conjugate to...
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