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 “pro±le” of our surface is a parabola, with vertex at the origin, opening up. (See ²igure 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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- Fall '08
- Calculus, different heights, horizontal slice