A Treatise On Plane Co-Ordinate Geometry As Applied to the Straight Line And ...
A Treatise On Plane Co-Ordinate Geometry As Applied to the Straight Line And ...
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The excentric angles of two points P and Q are ^ and 6' respectively; shew mat the area of the parallelogram formed by the tangents at the extremities of nie diameters through P and Q is -: — .,, ^ .. ; shew also that the area is least when P and Q are the extremities of conjugate dia- meters.
39. Shew that the equation to the locus of the middle points of all chords of the same length (2c) in an ellipse is 40. Chords of an ellipse are drawn at right angles to one another through the point whos...e co-ordinates are A, X; ; if CP, CQ, be the radu drawn from the centre parallel to the chords, and E, F, the middle points of the chords, shew that 41. Given the co-ordinates ofP, find those of the intersec- tion of the tangents at Pand 2). (See Fig. to Art. 192.) 42. Shew that the equation represents the tangents at P and -D, supposing a?', y' , the co- ordinates of P. (See Fig. to Art. 192.) 43. If CP, CD, be any conjugate diameters of an ellipse APBDA and PP, P2), be joined and also AD, A'P, these latter intersecting in 0, shew that BD OP ia a parallelogram.
What to read after A Treatise On Plane Co-Ordinate Geometry As Applied to the Straight Line And ...?
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To quickly assess the difficulty of the text, read a short excerpt:
The excentric angles of two points P and Q are ^ and 6' respectively; shew mat the area of the parallelogram formed by the tangents at the extremities of nie diameters through P and Q is -: — .,, ^ .. ; shew also that the area is least when P and Q are the extremities of conjugate dia- meters.
39. Shew that the equation to the locus of the middle points of all chords of the same length (2c) in an ellipse is 40. Chords of an ellipse are drawn at right angles to one another through the point whos...e co-ordinates are A, X; ; if CP, CQ, be the radu drawn from the centre parallel to the chords, and E, F, the middle points of the chords, shew that 41. Given the co-ordinates ofP, find those of the intersec- tion of the tangents at Pand 2). (See Fig. to Art. 192.) 42. Shew that the equation represents the tangents at P and -D, supposing a?', y' , the co- ordinates of P. (See Fig. to Art. 192.) 43. If CP, CD, be any conjugate diameters of an ellipse APBDA and PP, P2), be joined and also AD, A'P, these latter intersecting in 0, shew that BD OP ia a parallelogram.
What to read after A Treatise On Plane Co-Ordinate Geometry As Applied to the Straight Line And ...?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
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