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Mostly I'd like to look at the third part of the problem. I'm not sure if this is the correct way to derive the equation:

So, finding the length of a given vector given this inner product:

[itex]<(x,y),(x,y)> = 5x^2 + y^2[/itex].

Taking the length, we have

[itex]|(x,y)| = \sqrt{5x^2 + y^2}[/itex], which we define as equaling 1. Squaring both sides we find,

[itex]5x^2 + y^2 = 1[/itex]. I think this is the equation of the circle, but I'm not sure. If it is, then my picture has y-intercepts at 1,-1 and x-intercepts at -sqrt(1/5),sqrt(1/5).

Is this correct?

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# Inner products and Circles

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