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Libros Libros 1 a 10 de 11 sobre S through which any radius vector is drawn meeting the curves in P, Q, respectively....
" 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... "
A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and ... - Página 266
de Isaac Todhunter - 1858 - 316 páginas
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A treatise on plane co-ordinate geometry

Isaac Todhunter - 1855 - 299 páginas
...inversely 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...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...
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A treatise on plane co-ordinate geometry

1855 - 299 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...
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An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal ...

Norman Macleod Ferrers - 1861 - 184 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....
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A treatise on plane co-ordinate geometry

Isaac Todhunter - 1862
...inversely 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...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....
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A Collection of Problems and Theorems, with Hints, Results, and Occasional ...

Robert Henry Wright - 1865 - 128 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....
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A Book of Mathematical Problems on Subjects Included in the Cambridge Course

Joseph Wolstenholme - 1867 - 344 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...
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An Elementary Treatise on Conic Sections

Charles Smith - 1883 - 352 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...
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the methods of plane projective geometry based on the use of general ...

...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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Cartesian of the Plane

...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 =...
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A Textbook Of Analytical Geometry Of Two Dimensions

Jain, P.K. - 1986 - 362 páginas
...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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