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Unformatted text preview: a = c about the origin; in particular, L ( f,a 2 ) crosses the y-axis at the pair of points (0 , a ). To see how these circles t together to form the graph of f ( x,y ), we consider the intersection of the graph z = x 2 + y 2 with the yz-plane x = 0; the intersection is found by substituting the second equation in the rst to get z = y 2 and we see that the prole of our surface is a parabola, with vertex at the origin, opening up. (See igure 3.4 ) If instead we consider the function f ( x,y ) = 4 x 2 + y 2 , the horizontal slice at height c = a 2 > 0 is the ellipse x 2 ( a/ 2) 2 + y 2 a 2 = 1...
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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.
- Fall '08