An Elementary Treatise On Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions

Edward a Edward Albert Bowser

The book An Elementary Treatise On Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions was written by author Edward a Edward Albert Bowser Here you can read free online of An Elementary Treatise On Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is An Elementary Treatise On Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions a good or bad book?

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133 is «* + #» *y = — j— > which in the present example becomes l 2 4- l 2 1 Digitized by LiOOQ IC EXAMPLES.
211 3. Find the species and situation of the locus & _ 2xy + f — Sx + 16 = 0, and transform and construct a 2 — 4ac = 0; therefore the locus is a parabola.
The transformation is effected by Art. 146.
tan 20 = -— a —c = -co; .-. = 45°.
(1) Fig. 101.
Hence the new axis of x (Ox) is inclined to the old at an angle of 45°.
c' = i(l + l + Vi) = 2 [Art 143, (7)'] ; [here we take the minus valu...e of V& + (a — c) 2 because we squared — 2 to get ¥\ d' = $ (_ 8V2 + 0) = — 4V2 [Art 146, (2)'].
a' = f/g (8) = 4V2 [Art 146, (2)'].
Therefore, turning the axes OX and OY through 45°, (1) becomes fyt - Wtx + Wty + 16 = [Art. 146, (3)], or f — 2 V&z + 2 v% +8 = 0. (2) Now transform to parallel axes, OV and 0'y\ From (5) and (6) of Art. 146, we have y' = - V2, a/ = |V2, which in (4) of Art. 146 gives %

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