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" The triangle whose angular points are the focus of a conic and the intersections of the tangent and the diameter at any point with the axis and the directrix respectively has its orthocentre at the point in which the tangent meets the directrix. 57. Given... "
The Doctrine of Germs, Or, The Integration of Certain Partial Differential ... - Page 42
by Samuel Earnshaw - 1881 - 108 pages
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An Introduction to the Ancient and Modern Geometry of Conics: Being a ...

Charles Taylor - Mathematics - 1881 - 488 pages
...meet the direction of PS in U, then PU= \ QQ'. 47. If the normal to a conic at P meet the axis in G, and if SY the focal perpendicular upon the tangent...the directrix in Q, the locus of the intersection of Q 0 and SP will be a conic. 59. Deduce from Art. 16 that the square of the ordinate at any point of...
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An Introduction to the Ancient and Modern Geometry of Conics: Being a ...

Charles Taylor - Mathematics - 1881 - 512 pages
...intersections of the tangent and the diameter at any point with the axis and the directrix respectively has ita -orthocentre at the point in which the tangent meets...drawn at right angles to SP to meet the directrix in $, the locus of the intersection of QO and SP will be a conic. 59. Deduce from Art. 16 that the square...
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An Elementary Treatise on Conic Sections

Charles Smith - Conic sections - 1883 - 452 pages
...recta are to that of the original conic as ^/2 : 1 and 1 : ^/2 respectively. 9. Given the focus and directrix of a conic, shew that the polar of a given...point with respect to it passes through a fixed point. 10. If two conies have a common focus, shew that two of their common chords will pass through the point...
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The Elementary Geometry of Conics

Charles Taylor - Conic sections - 1883 - 164 pages
...has its orthocentre at the point in which the tangent meets the directrix. 53. Given the focus and directrix of a conic, shew that the polar of a given...point with respect to it passes through a fixed point. 54. Deduce from Art. 16 that the square of the ordinats at any point of a conic varies either as the...
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An Elementary Treatise on Analytical Geometry: With Numerous Examples

W. J. Johnston - Geometry, Analytic - 1893 - 462 pages
...focus and a common tangent consists of two circles. 26. Given the focus and directrix of a conic ; show that the polar of a given point with respect to it passes through a fixed point. 27. A circle circumscribes the triangle formed by tangents to a parabola at three points A, B, C. If...
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The Elements of Coordinate Geometry

Sidney Luxton Loney - Coordinates - 1896 - 447 pages
...angle at the centre if the point lie on the conic 7. Given the focus and directrix of a conic, prove that the polar of a given point with respect to it passes through another fixed point. 8. Prove that the locus of the centres of conies which touch the axes at distances...
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - Examinations - 1899 - 348 pages
...point, and its polar with respect to the conic. Given the focus and the directrix of a conic, show that the polar of a given point with respect to it passes through a fixed point. (60.) 84. All conies circumscribing a triangle and passing through its orthocentre have their asymptotes...
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An Elementary Treatise on Conic Sections by the Methods of Co-ordinate Geometry

Charles Smith - Conic sections - 1916 - 466 pages
...recta are to that of the original conic as ^/2 : 1 and 1 : ^2 respectively. 9. Given the focus and directrix of a conic, shew that the polar of a given...point with respect to it passes through a fixed point. 10. If two conies have a common focus, shew that two of their common chords will pass through the point...
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Coordinate Geometry: Polar Coordinates Approach

Mukut Mani Tripathi - Mathematics - 2005 - 166 pages
...than, equal to or greater than e. D Example 10. Given the focus and the directrix of a conic, show that the polar of a given point with respect to it passes through a fixed point. Solution. The conics may be taken as de — = 1 + e cos0, (1) r where the focus is the pole and directrix...
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A Textbook Of Analytical Geometry Of Two Dimensions

Jain, P.K. - Geometry, Analytic - 1986 - 378 pages
...so that SM—SN—l. Prove that PR touches the 20. Given the focus and directrix of a conic, prove that the polar of a given point with respect to it passes through a fixed point. 21 . Prove that the equation of the pair of tangents which can be drawn to the conic —=l+e cos 6...
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