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)#