Elementary Mathematical Analysis, a Text book for First Year College Students

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(2) Calling the constant value of rir^ = c', we have, as the Cartesian equation of the locus.
ly' + (x - a)'] [y^ + {x + a)'] = c\ (3) 394 ELEMENTARY MATHEMATICAL ANALYSIS [§223 Fig. 162. — The lemniscate and the Cassinian ovals.
which may be written (2/2 + x' + a^y - 4^a^x^ = c* (4) (j;2 + 2,2)2 4- 2aV + 2a?y^ + a a there is but a single oval.
The curves are shown in Fig. 162. These curves give the form of the equipotential surfaces in a field around two positively or two negatively charged pa
...rallel wires.
(2) Construct the curve such that the ratio of the distances of any of the curve from two fixed points is constant. Let the two fixed points be A and B, Fig.


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