An elementary treatise on analytical geometry : embracing plane co-ordinate geometry, and an introduction to geometry of three dimensions (1869)
Johnson, William Woolsey, 1841-1927 · Philadelphia : J.B. Lippincott · leaf 187
ely, A tan 4>. Y — B sec 0 . X = — ABand A sec <p . Y — B tan <p . X == AB, are the equations of tangents at P and P the vertices of conjugate diameters, since the value of <p for these points is the same. In the figure, P and P are so taken that <p is in the first quadrant. These… … sec <p — tan <ft sec <p — tan <p Combining the equation of the asymptote with the second equation,we find the same values of X and Y; that is, the same point ofintersection. The four tangents at the vertices of the conjugate diametersevidently form a parallelogram with centre at C. Each…
Geometry, Analytic
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