Elements of Analytic Geometry
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In our eReader you can find the full English version of the book. Read Elements of 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 Elements of Analytic Geometry
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2. Reduce each of the following equations to one of the forms in 244. (a)xy=-2. (b) 6z 2 - bxy - 6 y* = 0.
(c) 3z 2 -10zy + 3?/ 2 + 8 = 0. (d) 13x 2 - lOzy + 13y 2 - 72 = 0.
159. Transformation to Parallel Axes. To transform the general equation of the second degree (1), 154, to parallel axes through any point (X Q, i/ ), we have to substitute ( 13) the resulting equation is where the new constant term is (7) C' = Ax* + 2Hx (&0 + B It thus appears that after any translation of the coordinate sy...stem : (a) the coefficients of the terms of the second degree remain unchanged ; (6) the new coefficients of the terms of the first degree are linear functions of the coordinates of the new origin ; (c) the new constant term is the result of substituting the coordinates of the new origin in the left-hand member of the original equation.
156 PLANE ANALYTIC GEOMETRY [VIII, 160 160. Transformation to the Center. The transformed equa- tion will contain no terms of the first degree, i. E. It will be of the form (8) Ax' 2 + 2 Hx'y' + By' 2 + C' = 0, if we can select the new origin (X Q, y Q ) so that (9) This is certainly possible whenever i ', and we then find : Mm FH-GB GH-FA \1-\J) XQ - As the equation (8) remains unchanged when x', y f are replaced by x', y', respectively, the new origin so found is the center of the curve ( 133).
What to read after Elements of Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Alexander Ziwet to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
2. Reduce each of the following equations to one of the forms in 244. (a)xy=-2. (b) 6z 2 - bxy - 6 y* = 0.
(c) 3z 2 -10zy + 3?/ 2 + 8 = 0. (d) 13x 2 - lOzy + 13y 2 - 72 = 0.
159. Transformation to Parallel Axes. To transform the general equation of the second degree (1), 154, to parallel axes through any point (X Q, i/ ), we have to substitute ( 13) the resulting equation is where the new constant term is (7) C' = Ax* + 2Hx (&0 + B It thus appears that after any translation of the coordinate sy...stem : (a) the coefficients of the terms of the second degree remain unchanged ; (6) the new coefficients of the terms of the first degree are linear functions of the coordinates of the new origin ; (c) the new constant term is the result of substituting the coordinates of the new origin in the left-hand member of the original equation.
156 PLANE ANALYTIC GEOMETRY [VIII, 160 160. Transformation to the Center. The transformed equa- tion will contain no terms of the first degree, i. E. It will be of the form (8) Ax' 2 + 2 Hx'y' + By' 2 + C' = 0, if we can select the new origin (X Q, y Q ) so that (9) This is certainly possible whenever i ', and we then find : Mm FH-GB GH-FA \1-\J) XQ - As the equation (8) remains unchanged when x', y f are replaced by x', y', respectively, the new origin so found is the center of the curve ( 133).
What to read after Elements of Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Alexander Ziwet to read onlineMoreLess
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