 | Mathematics - 1836 - 600 pages
...Rules for finding the logarithms of numbers. (50). QUESTION VI. By . Def. A diameter of a curve is the locus of the middle points of a system of parallel chords. . Find the equations of the diameters of the curves represented by the general equation of the second... | |
 | John Hymers - Conic sections - 1837 - 486 pages
...center is С and radius equal to V* a* + b3The Ellipse referred to its conjugate Diameters. 138. To find the locus of the middle points of a system of parallel chords. Let the chords be parallel to a line CD (fig. 45) through ¿he center, whose equation is у = mx ;... | |
 | Michel Chasles - Cone - 1837 - 564 pages
...center is С and radius equal to v a2 + W. The Ellipse referred to its conjugate Diameters. 138. To find the locus of the middle points of a system of parallel chords. Let the chords be parallel to a line CD (fig. 45) through the center, whose equation is y = mx ; then... | |
 | English literature - 1840 - 528 pages
...Sln T~ ' . c AB C . a+b and sin - . cos — — — = sin — . sin -•;;--• m im £i £i 8. Find the locus of the middle points of a system of parallel chords of the curve whose equation is ax* + bxy + cy* + dx -f ey +f = 0. Hence shew that the curve has generally... | |
 | Education - 1840 - 468 pages
...— - — = cos — . sin — — t c A — B Co + i. and sin — . cos • — = sin - . sin P. Kind the locus of the middle points of a system of parallel chords of the curve whose equation is air* + bxy + cy? + dx + ey + / = U. Hence show timi the curve has generally... | |
 | Matthew O'Brien - Geometry, Algebraic - 1844 - 270 pages
...making an angle whose tangent is - cot 0 I ». e. an angle 0 + ~ ) with the axis of x. 134. CОЕ. The locus of the middle points of a system of parallel chords is called the diameter of those chords ; hence, by what we have just proved, the diameter of any system... | |
 | Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...tangents to the latter. Find the locus of the intersections of the latter pairs of tangents. 15. Find the locus of the middle points of a system of parallel chords drawn between an hyperbola and the conjugate hyperbola. 16. If a pair of conjugate diameters of an... | |
 | John Hymers - Geometry, Analytic - 1848 - 368 pages
...proposed equation must be capable of being resolved into two rational factors of the first degree. 136. The locus of the middle points of a system of parallel chords of any proposed surface is called its diametral surface. This surface will have several sheets, if each... | |
 | William Walton - Coordinates - 1851 - 458 pages
...hence QR.QR' = W. Similarly jr.gr' = 26'2. De la Hire: Sectiones Conicce, lib. IV. prop. 34. 2. To find the locus of the middle points of a system of parallel chords drawn between an hyperbola and the conjugate hyperbola. Let two conjugate diameters be taken as axes... | |
 | George Hale Puckle - Conic sections - 1856 - 286 pages
...and the polar of P respectively make with the transverse axis, then tan (p . tan <t>' = 1 . 48. Find the locus of the middle points of a system of parallel chords drawn between an hyperbola and the conjugate hyperbola. SECTION X. The Parabola. 193. WE saw (Art.... | |
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The locus of the middle points of a system of parallel chords in a parabola is called a diameter. 
