Dowling, L. Wayland (Linnaeus Wayland), b. 1867, Turneaure, F. E. (Frederick Eugene), 1866- · New York, H. Holt and company · leaf 164
s. For example, consider the equation X- + 2 xy + 2 y^ — 4 = 0. Here tan 20 = -^-^ = -^— = - 2, from which we get 8 = 58° 17, nearly,a — b 1 — 2 If the axes are rotated through the angle 8, the term in xy will drop out. The coefficients of x^^ and ?/ are the roots of (14) which becomes, in this… … 2(3-V5) 2(3+\/y) The locus is, therefore, an ellipse whose semiaxes are V2(3 — VS) andV2(3 +VE). The major axis coincides with the new F-axis (Fig. 89). 148 EQUATIONS NOT IN STANDARD FORM [Chap. VIII. EXERCISES 1. Determine the nature of the locus of the equation 5X+2xy + 5y^ = 12.Find the angle…
Geometry, Analytic
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