| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| |