 | Isaac Todhunter - 1855 - 332 páginas
...as the latus rectum ; find the locus of these points. 21. Two conic sections have a common focus 8 through which any radius vector is drawn meeting the...lines are inversely proportional to the corresponding excentrities. 22. A line is drawn cutting an ellipse in the points P, p . let Q be either of the points... | |
 | Norman Macleod Ferrers - 1861 - 200 páginas
...which give the focus in that case. EXAMPLES. 1. HAVING given a focus and two points of a conic section, prove that the locus of the point of intersection of the tangents at these points will be two straight lines, passing through the focus, and at right angles to each other.... | |
 | Isaac Todhunter - 1862 - 376 páginas
...as the latus rectum ; find the locus of these points. 21. Two conic sections have a common focus S through which any radius vector is drawn meeting the...directrices of the conic sections, and that the sines 01 the angles which it makes with these lines are inversely proportional to the corresponding excentricities.... | |
 | Robert Henry Wright - 1865 - 174 páginas
...directed to that infinitely distant point. 298. A focus and two points of a conic section being given, prove that the locus of the point of intersection of the tangents at these points will be two straight lines passing through the focus and at right angles to each other.... | |
 | Joseph Wolstenholme - 1867 - 368 páginas
...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... | |
 | Charles Smith - 1883 - 388 páginas
...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... | |
 | 1915 - 412 páginas
...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 - 1916 - 466 páginas
...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 páginas
...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 =... | |
 | E. A.. Maxwell - 258 páginas
...at A and B. Through a given point C on AB a variable straight line is drawn, cutting OA, OB in P and Q respectively. Prove that the locus of the point of intersection of the other tangents from P and Q is a straight line through 0. [CS] 10. A conic touches the sides QR, RP,... | |
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Two conic sections have a common focus 8 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. 
