Linear Algebra Solutions 83

Linear Algebra Solutions 83 - = 0 and = 1 / 2. Then (8)...

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In terms of x, y coordinates, equation (7) becomes (3 x - ( y - 1)) 2 = 0 , or 3 x - y + 1 = 0 . (iii) Consider the equation x 2 + 4 xy + 4 y 2 - x - 2 y - 2 = 0 . (8) Arguing as in the previous examples, we Fnd that any translation x = x 1 + α, y = y 1 + β where 2 α + 4 β - 1 = 0 has the property that the coe±cients of x 1 and y 1 will be zero in the transformed version of equation (8). Take
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Unformatted text preview: = 0 and = 1 / 2. Then (8) reduces to x 2 1 + 4 x 1 y 1 + 4 y 2 1-9 4 = 0 , or ( x 1 +2 y 1 ) 2 = 3 / 2. Hence x 1 +2 y 1 = 3 / 2, with corresponding equations x + 2 y = 2 and x + 2 y =-1 . 86...
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