I have to show that $2r+r\cos\theta =1$ describes a cylinder.
I try moving the equation to cartesian coordinates and I get$\ 3x^2+4y^2-2x=1$, after that I don't know what to do, any help would be appreciated.
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2Hint: Complete the squares – DiegoMath Jun 05 '19 at 22:52
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1I did, but I got to an equation that describes an ellipse, shouldn't it be a circle? – Demian Jimenez Jun 05 '19 at 22:54
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Did you mean $...\color{red}+2x= 1$? – J. W. Tanner Jun 05 '19 at 22:57
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yes, my mistake – Demian Jimenez Jun 05 '19 at 22:58
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maybe it's an elliptic cylinder – J. W. Tanner Jun 05 '19 at 23:00
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Does it need to be a circle? – Demian Jimenez Jun 05 '19 at 23:00
1 Answers
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Note that $$1= 3x^2+4y^2-2x=3\left(x-\dfrac{1}{3}\right)^2+4y^2-\dfrac{1}{3}\Rightarrow \frac{\left(x-\dfrac{1}{3}\right)^2}{4}+\frac{y^2}{3}=1.$$
Then, you have an elliptic cylinder.
DiegoMath
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