Introduction to Quaternions

Cover Introduction to Quaternions
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53. ] CONES AND THEIR SECTIONS. 109 {d) Find the locus of the intersection with the tangent of the perpendicular on it from the vertex.
To solve this last problem let it be the vector perpendicular on the tangent from A, then by (8) and the equation of the tangent gives, putting tt + - in place of 77 in (5) and multiplying by 2, 2STrcj>p + -iSa-^TT + 2Sa-^p = 1, we have also From these three equations we have to eliminate x and p. The first gives Sa-JT = X, which gives x, and STrp)'\ which
... substituted in the second gives 1x{^pf + 2/S'a-V + 2So. -^p = 1. Also, substituting or{(^pY for Sp4>p (equation 7), the third equation gives a2(c/)p)2 + 2

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