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" F, and the product of the distances of any point of the curve from the three asymptotes is in a constant ratio to its distance from the line F. "
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 136
by George Salmon - 1852 - 316 pages
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 338 pages
...curve again. 137. Equation (2) also includes the following (3) ACE - k2F = 0, or A(C2 E2) = A2F, an equation containing nine constants, and therefore...let BDF coincide, and the equation becomes (4) ACE - B2 = 0, an equation also containing nine constants. A, C, E are (Art. 42) tangents at points of inflexion,...
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The Messenger of Mathematics, Volume 15

Mathematics - 1886 - 258 pages
...(8), where SE (ЗА - a - b - c) (z* + y') - 2 [k (a + b + c} - ab - be - ca] x from which we see that the product of the distances of any point of the curve from the three foci is in a constant ratio to the cube of the tangent from the same point to a director circle 8....
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Briot and Bouquet's Elements of Analytical Geometry of Two Dimensions

Charles Briot, Bouguet (M., Jean Claude) - Geometry, Analytic - 1896 - 598 pages
...proportional to the distances of any point (x, y) from the sides of the quadrilateral, it follows that the product of the distances of any point of the curve from the two opposite sides ab, cd of the inscribed quadrilateral is to the product oj the distances of the...
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Introduction to the Theory of Analytic Functions

James Harkness, Frank Morley - Analytic functions - 1898 - 336 pages
...with centre a. Then, if lP = a, we have yt-fi—x— a, and iy-^l \y+b\ = \x—a\ = a. constant. Thus the product of the distances of any point of the /-curve from two fixed points b, — b is constant. Such a curve is called a cassinian. Fig. 62 Fig. 62. shows the...
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