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Plugging in gives the following plot: http://www.wolframalpha.com/input/?i=x%5E2-y%5E2+%3D+1

Yet, it seems that choice [e] was incorrect according to the answer key. But choice [d] (as per the answer key) gives the following plot: http://www.wolframalpha.com/input/?i...%2By%5E2+%3D+1

What am I missing?

 Michael Reach 05-07-2013 02:01 PM

I think you are adding the constant term on the wrong side of the equation.
w0*1 + w1*x^2 + w2*y^2
To get these to add up to +1 in the middle of the plot (x=0, y=0, say), we'll need w0 = -1.
Then to get negative values as x increases ( --> -1 on the right side of of the plot), we'll need w1 to be negative. And so on.

 dlammerts 05-07-2013 02:06 PM

I made the same mistake and finally figured out that the shape of the hyperbolas in your two plots is determined by the fact that your w0 is negative (just rearrange your formulas into the h = sign(w0 + w1*x1^2 + w2*x2^2) form to see this). The "inner" part of your hyperbolas assumes the value -1 instead of +1 as required. If your plot answer [d] with a positive w0, which makes the inner region assume the value +1, then the the orientation of the hyperbolas flips to the required shape:
http://www.wolframalpha.com/input/?i...Bx2%5E2+%3D-+1

Dirk

 Elroch 05-07-2013 02:07 PM

What happens if you shunt everything to the same side of the equation?

[EDIT: snap, Michael :) ]

Thank you everyone for the replies. It is somewhat annoying to make a mistake on an "easy" question :)

 Michael Reach 05-07-2013 08:35 PM