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Engineering Calculus Notes 143

Engineering Calculus Notes 143 - 131 2.1 CONIC SECTIONS...

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2.1. CONIC SECTIONS 131 simple examples. First, the substitution x mapsto→ x 1 y mapsto→ y 2 into the model parabola equation y = x 2 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
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