Bailey, Frederick H. (Frederick Harold), 1865- · Boston, London, Ginn & Co. · leaf 310
this, and at the sametime we will deduce a rule by which we can often tell by in-spection that a given equation represents a surface of revo-lution. 1. The circle x^ + z^=a^ Fig. 13, is rotated about OX asan axis, forming the sphere of radius a. If Pi is a point of the circle, then the equation of… … Fig. 13. If, now, X, y, z are the coordinates of P, OL = x andLP = Vy^+ z^. Therefore the equation of the sphere is x^ + y^ + z = a^- Here we have formed the equation of the sphere from tliatof the circle by replacing z by Vy^ + z^. 2. The hyperbola — — - = 1, Fig. 14, is rotated about OX.The…
Geometry, Analytic
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