 The exterior angle between any two intersecting tangents to a parabola, is equal to the angle which either of them subtends at the focus...  Science Examination Papers - Page 53by Great Britain. Education Department. Department of Science and Art - 1908Full view - About this book
 | Charles Taylor - Conic sections - 1863 - 262 pages
...perpendicular distance of R ,from the directrix. PROP. III. The external angle between any two tangents is equal to the angle which either of them subtends at the focus. Let the tangents at P, Q, intersect in R, and meet the axis in T, Z7, respectively. Take any point... | |
 | Charles Taylor - Conic sections - 1880 - 152 pages
...9), SA : SY=SY : SP, or SY* = SA . SP, and SY* varies as SP, as was to be proved. PROPOSITION IX. 27. The exterior angle between any two tangents to a parabola...angle which either of them subtends at the focus. Let the tangents at P and Q intersect in T, and let them meet the axis in p and q. Take any point O... | |
 | Samuel Earnshaw - Differential equations, Partial - 1881 - 602 pages
...focal perpendiculars upon them. PROPOSITION IX. 28. The exterior angle between any two intersecting tangents to a parabola, is equal to the angle which either of them subtends at the focus ; and the inclination of either tangent to the axis is equal to that of the other to the focal distance... | |
 | Charles Taylor - Mathematics - 1881 - 486 pages
...focal perpendiculars upon them. PROPOSITION IX. 28. The exterior angle between any two intersecting tangents to a parabola is equal to the angle which either of them subtends at the focus ; and the inclination of either tangent to the axis is equal to that of the other to the focal distance... | |
 | Charles Smith - Conic sections - 1883 - 388 pages
...- cos 0 - e=cos a, and - sin 0 = sin a. By the elimination of a we get EXAMPLES ON CHAPTER VIII. 1. The exterior angle between any two tangents to a parabola is equal to half the difference of the vectorial angles of their points of contact. 2. The locus of the point of... | |
 | Thomas Jay Evans, W. W. F. Pullen (Wh.Sc., A.M.I.C.E.) - Geometry, Plane - 1897 - 420 pages
...Draw a parabola touching the three sides of the triangle, and passing through P. NB — The external angle between any two tangents to a parabola is equal to the angle which either subtends at the focus. Describe a circle passing through ABC; the focus F will lie on this circle.*... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...conditions are these data respectively equivalent ? 13. The exterior angle between any two intersecting tangents to a parabola is equal to the angle which either of them subtends at the focus. Prove that if S be the focus and PQ the points in which two fixed tangents are cut by a third, the... | |
 | Charles Smith - Conic sections - 1916 - 466 pages
...equation is found by eliminating a between (i) and (ii). The equation is EXAMPLES ON CHAPTER VIIL 1. The exterior angle between any two tangents to a parabola is equal to half the difference of the vectorial angles of their points of contact. 2. The locus of the point of... | |
 | John F. Dowsett - Geometry - 1927 - 378 pages
...ellipse will describe circles having the foci of the fixed ellipse as centres. (B. o. E.) 19. Show that the exterior angle between any two tangents to...the ends of any focal chord in P and Q; show that PSQ is a right angle, S being the focus. (B. o. E.) 20. Prove that in an ellipse the tangent at any... | |
 | Jain, P.K. - Geometry, Analytic - 1986 - 378 pages
...point as a focus and touching a fixed line. Prove that the locus of their centres is a conic. 18 . Prove that the exterior angle between any two tangents to a parabola is half I*"* difference of the vectorial angles of their point of contact. 19. P, Q, R are three points... | |
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