Tanner, J. H. (John Henry), b. 1861, Allen, Joseph · New York, American Book Co · leaf 169
, (1) where A and B have the same sign, and neither of them is zero.Conversely, au equation of this form represents an ellipse theaxes of which are parallel to the coordinate axes. A numer-ical example will suggest the general proof. Example. Given the equation ia^ + 9y^ — 16 x-f IS?/ —11 = 0, to… … 4ie»-16a! + 16 + 92/» + 182/+ 9=11 + 16 + 9,that is 4(a; - 2f + 9{y +1)^ = 36; hence ^:^ + (^L+lH= l. 32 T- 2= This equation is of the form [36], and, therefore,its locus has the geometric property given in Art. 88,and is an ellipse. Its center is the point (2, —1);its major axis is parallel to the…
Geometry, Analytic
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