Analytic Geometry
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In our eReader you can find the full English version of the book. Read Analytic Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Analytic Geometry
What reading level is Analytic Geometry book?
To quickly assess the difficulty of the text, read a short excerpt:
92 where the primes have been dropped.
The angle through which the axes have been rotated is given by the equation tan 61=-- =1, h Therefore d = 45^. Figure 92 shows the locus and the three sets of axes.
EXERCISES 1. Reduce the following equations to the standard form . Determine the angle through which it is necessary to rotate the axes in order to remove the term in xy^ and the coordinates of the vertex referred to the original axes : (a) x2 - 2 a;?/ -h 2/2 - 8 X + 16 = 0.
(6) x2 — 2 x?/ + 2/...^ + 2 X — 2/ - 1 = 0.
(c) 4 x2 + 4 X2/ -I- 2/^ — 4 X = 0.
(d) 9 x2 + 12 X2/ -h 4 2/2 - 2 2/ = 0.
(e) x2 -h 4 X2/ + 4 2/2 - 6 X -I- 8 2/ -t- 1 = 0.
Art. 116] THIRD CASE, afc - /i^ = AND hf - bg = 155 116. Third case, ab—h^=0 and hf—bg=0. Since ah — h^ is again eqnal to zero, the general equation is reducible to the form (1), or the form (2), of the preceding article, according as h is positive or negative. But here hf—bg = and af — hg=Q.
Hence, if h is positive, /' = ; and if 7i is negative, g' = 0.
What to read after Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Dowling, L. Wayland (Linnaeus Wayland), B. 1867 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
92 where the primes have been dropped.
The angle through which the axes have been rotated is given by the equation tan 61=-- =1, h Therefore d = 45^. Figure 92 shows the locus and the three sets of axes.
EXERCISES 1. Reduce the following equations to the standard form . Determine the angle through which it is necessary to rotate the axes in order to remove the term in xy^ and the coordinates of the vertex referred to the original axes : (a) x2 - 2 a;?/ -h 2/2 - 8 X + 16 = 0.
(6) x2 — 2 x?/ + 2/...^ + 2 X — 2/ - 1 = 0.
(c) 4 x2 + 4 X2/ -I- 2/^ — 4 X = 0.
(d) 9 x2 + 12 X2/ -h 4 2/2 - 2 2/ = 0.
(e) x2 -h 4 X2/ + 4 2/2 - 6 X -I- 8 2/ -t- 1 = 0.
Art. 116] THIRD CASE, afc - /i^ = AND hf - bg = 155 116. Third case, ab—h^=0 and hf—bg=0. Since ah — h^ is again eqnal to zero, the general equation is reducible to the form (1), or the form (2), of the preceding article, according as h is positive or negative. But here hf—bg = and af — hg=Q.
Hence, if h is positive, /' = ; and if 7i is negative, g' = 0.
What to read after Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Dowling, L. Wayland (Linnaeus Wayland), B. 1867 to read onlineMoreLess
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