Schmall, Charles Nelson. [from old catalog] · New York, D. Van Nostrand company · leaf 227
Fig. 127. OX and OY are the asymptotes, <^ is the semi-angle be-tween them. P is (x, y) to the former axes, (x% y) to thenew axes. a; = ON + ISTL + LQ = OK cos <^ + EL cos (^ + LP cos ^= (OR + PR) cos <^, .. x — {x -\- y) cos <^. y = PQ = PL sin (^ = (PR - LR) sin «j!> = (PR - OR)… … {x + i/Y cos^ 4> _ (/ - xy sin2 (^ _ Also, since tan <^ = sin ^ =cos <^ = Va2 + &2 a Va2 + h Substituting also these values above, we finally obtain, after(Iroppiug accents, 4 xj^ = a2 -[- Z>2 as the required equation.The conjugate hyperbola is Note. — In the figure of § 159, if the…
Geometry, Analytic
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