How do you find an equivalent equation of $x^2 + 4y^2 = 4$ in polar coordinates?

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Answer 1 · 2018-04-11T14:10:50

$r^2=4/(cos^2theta+4sin^2theta)$

$r=sqrt(4/(cos^2theta+4sin^2theta))=2/sqrt(cos^2theta+4sin^2theta)$

We'll use the two formulae:
$x=rcostheta$
$y=rsintheta$

$x^2=r^2cos^2theta$
$y^2=r^2sin^2theta$

$r^2cos^2theta+4r^2sin^2theta=4$

$r^2(cos^2theta+4sin^2theta)=4$

$r^2=4/(cos^2theta+4sin^2theta)$

$r=sqrt(4/(cos^2theta+4sin^2theta))=2/sqrt(cos^2theta+4sin^2theta)$

How do you find an equivalent equation of x^2 + 4y^2 = 4x^2 + 4y^2 = 4 in polar coordinates?