 | Isaac Todhunter - Geometry - 1855 - 332 pages
...'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 — <p) least... | |
 | Isaac Todhunter - Conic sections - 1858 - 334 pages
...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 sm (9 — <p)... | |
 | Duncan Farquharson Gregory, Robert Leslie Ellis - Mathematics - 1865 - 320 pages
...applications of the theory. MATHEMATICAL NOTE.' THE area of the parallelogram formed by tangents applied at the extremities of any two conjugate diameters of an ellipse is constant. Let x, y be the coordinates of the extremity of one diameter, and x\ y those of the other ; 0, & the... | |
 | 1866 - 390 pages
...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... | |
 | James White - Conic sections - 1878 - 160 pages
...their 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 4<z6. It is evident... | |
 | Rufus B. Howland - Conic sections - 1887 - 76 pages
...: OE : F'D ; hence FG : I'L : : OE : F'D, or PL • OE = PL • PK= FG • F'D = FC2. THEOREM XXVI. The area of the parallelogram formed by the tangents at the extremities of two conjugate diameters of an ellipse is constant, and equals the rectangle on the axes. Let PC be... | |
 | Sir Asutosh Mookerjee - Conic sections - 1893 - 197 pages
...and Note on Tangent- Proper lies, Ex. I., 1.] PR . PR' : QR . QR'=OP* : OQ' 2 . * PEOPOSITION XXXV. The area of the parallelogram formed by the tangents at the extremities of a pair of conjugate diameters is constant. (GD.PF=GA.CB.) The tangents at the extremities of two conjugate... | |
 | Sidney Luxton Loney - Coordinates - 1896 - 447 pages
...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... | |
 | 1903 - 788 pages
...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... | |
 | George Alexander Gibson - Algebra - 1904 - 204 pages
...the coordinates of F are ~ a2sin20 + &2cos20 ' and that CF= J(a* +/) = ^. 24. Show from example 23 that the area of the parallelogram formed by the tangents at the ends of two conjugate diameters PCP, DCLf is constant, and equal to 4a6 or A A'. BB-, the rectangle... | |
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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 ab. 
