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" Prove that the area of the parallelogram formed by the tangents at the extremities of two conjugate diameters of an ellipse is constant, and is equal to 4 06. "
An Elementary Treatise on Graphs - Página 156
de George Alexander Gibson - 1904 - 183 páginas
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A Treatise on Plane Co-ordinate Geometry: With Numerous Examples ...

Isaac Todhunter - 1855 - 332 páginas
...'2 ' 172 • abab 3§. The excentric angles of two points P and Q are <f> and A' respectively; shew that the area of the parallelogram formed by the tangents at the extremities of the diameters through P and Q is —. — 7-77 -^ ; shew also that the area is sin (<p...
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A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and ...

Isaac Todhunter - 1858 - 334 páginas
...sin4 a + &2 cos2 a. 38. The excentric angles of two points P and Q are <£ and <ft respectively; shew that the area of the parallelogram formed by the tangents at the extremities of the diameters through P and Q is — — rr, — -r-. ; shew also that the area is 0...
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Mathematical Questions with Their Solutions: From the ..., Volumes 4-6

1866 - 390 páginas
...the semi-axes of an ellipse, and <j>, </>'the eccentric angles of two points P, Q on the curve; prove that the area of the parallelogram formed by the tangents at the ends of the diameters through P and Q is 4a6 ccsec (</>' — <J>). Solution by J. McDoWEiL, HA ; SW BBOMHELD...
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Mathematical Questions and Solutions, from the "Educational Times ..., Volume 6

W. J. C. Miller - 1866 - 126 páginas
...semi-axes of an ellipse, and ф, ф ' the eccentric angles of two points P, Q on the curve ; prove that the area of the parallelogram formed by the tangents at the cuds of the diameters through P and Q is 4ah ccsec (ф' - ф). Solution by J. McDowEbb,'MA ; SW BBOMÏIELD;...
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Conic Sections, Treated Geometrically

William Henry Besant - 1869 - 304 páginas
...CD :: AC : BC. For the proofs of these relations, see Art. (79). Observe also that 124. PBOP. XXVII. The area of the parallelogram formed by the tangents at the ends of conjugate diameters is equal to the rectangle contained by the axes. Let CP, CD be the semi-diameters,...
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An elementary manual of coordinate geometry and conic sections

James White - 1878 - 160 páginas
...extremities, is constant. The triangle TC T' = ia'. V sin TCT= ab = io6. From this it evidently follows that the area of the parallelogram formed by the tangents at the extremities of a pair of conjugate diameters, being equal to eight times the triangle, is equal to...
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An Elementary Treatise on Conic Sections

Charles Smith - 1883 - 452 páginas
...given straight lines, shew that the fourth side will also be parallel to a fixed straight line. 41. The area of the parallelogram formed by the tangents at the ends of any pair of diameters of an ellipse varies inversely as the area of the parallelogram formed by joining...
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The Elements of Coordinate Geometry

Sidney Luxton Loney - 1896 - 447 páginas
...similar ellipse. 22. The eccentric angles of two points P and Q on the ellipse are 01 and 02 ; prove that the area of the parallelogram formed by the tangents at the ends of the diameters through P and Q is and hence that it is least when P and Q are at the end of conjugate...
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Examination Papers: A Supplement to the University Calendar

1903 - 788 páginas
...axis, a point on the curve and the normal at that point, construct the focus and directrix. 4. Show that the area of the parallelogram formed by the tangents at the ends of two conjugate diameters of an ellipse is constant. If two conjugate diameters are given in position and magnitude, how can...
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Analytic Geometry, a First Course

William Henry Maltbie - 1906 - 156 páginas
...reduce the value of the product to 6 2 . 16. By aid of the last problem and problem 8, article 68, show that the area of the parallelogram formed by the tangents at the extremities of any pair of conjugate diameters of a central conic is independent of the position of...
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