Schmall, Charles Nelson. [from old catalog] · New York, D. Van Nostrand company · leaf 319
anhyperbola; any section through the axis consists of two inter-secting straight lines. 28. Sections of a cone. — We propose to determine the nature of any section of a coneby finding its equation referredto a pair of axes in the secantplane. APB is any section of a cone,through the ^/-axis and .-.… … SURFACES OF REVOLUTION 303 Let Z XOB = </), Z OKZ = 6>. Then, draw PM J_ OB, M.N ± OX. Now, 0]^ = OM cos <^, UN = OM sin ^, or X = x^ cos <^, 2: = Xi sin <l>, y = PM = y [since PM ± xz plane]. Substituting these values for x, y, z, in the equation of thecone, [^2(^2 ^ y2^ = (^ _…
Geometry, Analytic
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