 | Isaac Todhunter - 1855 - 376 pages
...a common focus S through which any radius vector is drawn meeting the curves in P, Q, respectively. Prove that the locus of the point of intersection of the tangents at P, Q, is a straight line. Shew that this straight line passes through the intersection of the directrices... | |
 | Isaac Todhunter - Conic sections - 1858 - 334 pages
...common fociis S through which any radius vector is drawn meeting the curves in P, Q, respectively. Prove that the locus of the point of intersection of the tangents at P, Q, is a straight line. Shew that this straight line passes through the intersection of the directrices... | |
 | Robert Henry Wright - Coordinates, Trilinear - 1865 - 174 pages
...—w = 0. ^XV^^+XX'^0. ..(10), ..(11), therefore which establishes the theorem. 119. Having given a focus and two points of a conic section, prove that the locus of the intersection of the tangents at these points will be two straight lines, passing through the focus,... | |
 | Joseph Wolstenholme - Mathematics - 1867 - 368 pages
...intersect in A, B, C, D • through D is drawn a straight line to meet the curves again in two points ; prove that the locus of the point of intersection of the tangents at these points is a curve of the fourth degree and third class, having cusps at A, B, C, and touching both conies.... | |
 | Isaac Todhunter - Conic sections - 1874 - 378 pages
...common focus 8 through which any radius vector is drawn meeting the curves at P, Q, respectively. Shew that the locus of the point of intersection of the tangents at P, Q, is a straight line. Shew that this straight line passes through the intersection of the directrices... | |
 | Charles Smith - Conic sections - 1883 - 388 pages
...parabola make angles with the axis such that the product of the tangents of their halves is constant; prove that the locus of the point of intersection of the tangents is a confocal parabola, 50. If the circle described on the chord PQ of a parabola as diameter cut the... | |
 | Education - 1915 - 412 pages
...17625.)— A circle touches a limaeon at P and Q, the points of contact being on different loops. Show that the locus of the point of intersection of the tangents at P and Q is a cissoid. Solution (I) by CE YOUNOMAN, MA Let S be the node and SOX a diameter of the directrix... | |
 | Charles Smith - Conic sections - 1916 - 466 pages
...parabola make angles with the axis such that the product of the tangents of their halves is constant ; prove that the locus of the point of intersection of the tangents is a confocal parabola. 50. If the circle described on the chord PQ of a parabola as diameter cut the... | |
 | 352 pages
...ellipse 3x2 + 4?/2 = 28 whose mid-point is the point (1, 1). Find also the length of this chord. 10. Prove that the locus of the point of intersection of the tangents at the ends of conjugate diameters of the ellipse a;2/a2 + 2/2/62 = 1 is the ellipse x2/a2 + i/2/62 =... | |
 | Jain, P.K. - Geometry, Analytic - 1986 - 378 pages
...the chord. Prove that the locus of the point of intersection of the normals is another parabola. 20. Prove that the locus of the point of intersection of the tangents to the parabola is a line parallel to j-axis. 21. If a chord of the parabola y"=4ax subtends a right... | |
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Prove that the locus of the point of intersection of the tangents at P, Q, is a straight line. Shew that this straight line passes through the intersection of the directrices of the conic sections, and that the sines of the angles which it makes with... 
