# Inner products and Circles

by TranscendArcu
Tags: circles, products
 P: 288 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: $<(x,y),(x,y)> = 5x^2 + y^2$. Taking the length, we have $|(x,y)| = \sqrt{5x^2 + y^2}$, which we define as equaling 1. Squaring both sides we find, $5x^2 + y^2 = 1$. 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?
 Sci Advisor P: 1,169 I think you're missing some terms from the length: <(x,y),(x,y)>=5x2+2(xy+yx)+y2
 P: 288 Whoops. You're right. My real equation is $5x^2 -2(xy+xy) +y^2 =1$. This changes shape of the circle (it's more elongated in quadrants I and III now), but the intercepts remain the same I think. No?
 Sci Advisor P: 1,169 Inner products and Circles I think if you do a rotation of the plain, you may be able to get rid of the mixed xy-terms.

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