The graph of the function f(x, y) = y^2 - x62 in 3-space is the hyperbolic parab

Question

The graph of the function f(x, y) = y^2 - x62 in 3-space is the hyperbolic paraboloid (saddle surface). The level curves or contours, have equations of the form y^2 - x^2 = k. the hyperbolic contours at the level of z = -4 are ________ The hyperbolic contours at the level of z = -1 are _________ The straight line contours at the level of z = 0 are _________ The hyperbolic contours at the level of z = 1 are _________ The hyperbolic contours at the level of z = 4 are _________ On the graph below, sketch and label by its k value each of the contours corresponding to k = -4, -1, 0, 1, 4.

Explanation / Answer

the hyperbolic contours at the level of z=-4 are y2-x2=-4

the hyperbolic contours at the level of z=-1 are  y2-x2=-1

the straight line contours at the level of z=0 are y2-x2=0

the hyperbolic contours at the level of z=1 are y2-x2=1

the hyperbolic contours at the level of z=4 are y2-x2=4

iam unable to upload image of contours

http://tinypic.com/r/nnr1w7/9

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