Engineering Calculus Notes 143

Engineering - 131 2.1 CONIC SECTIONS simple examples First the substitution x→x−1 y →y−2 into the model parabola equation y = x2 leads to

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Unformatted text preview: 131 2.1. CONIC SECTIONS simple examples. First, the substitution x→x−1 y →y−2 into the model parabola equation y = x2 leads to the equation y − 2 = (x − 1)2 ; we note that in the new equation, substitution of the point (1, 2) leads to the equation 0 = 0, and furthermore no point lies below the horizontal line through this point, y − 2 = 0: we have displaced the parabola so as to move its vertex from the origin to the point (1, 2) (Figure 2.9). (0, 3) (2, 3) y − 2 = (x − 1)2 (1, 2) (−1, 1) (1, 1) y = x2 (0, 0) Figure 2.9: Displacing a parabola Second, to move the ellipse x2 y 2 + =1 4 1 so that its center moves to (−2, 2), we perform the substitution x → x − (−2) = x + 2 y →y−2 (Figure 2.10) ...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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