Convert the equation #x^2+y^2/4=1# in polar form?

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Answer 1 · 2017-12-05T14:54:09

#r=4/sqrt(1+3cos^2theta)#

The relation between rectangular or Cartesian coordinates #(x,y)# and polar coordinates #(r,theta)# is given by

#x=rcostheta# and #y=rsintheta# i.e. #x^2+y^2=r^2#

Hence we can write #x^2+y^2/4=1# can be written as

#r^2cos^2theta+r^2/4sin^2theta=1#

or #r^2/4(4cos^2theta+sin^2theta)=1#

or #r^2(1+3cos^2theta)=4#

or #r=4/sqrt(1+3cos^2theta)#