How do you convert #r=4tanθ# into cartesian form?

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How do you convert #r=4tanθ# into cartesian form?

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Answer 1 · 2016-07-19T17:14:50

#x^4+x^2y^2-16y^2=0#

Explanation:

The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is given by #x=rcostheta#, #y=rsintheta#, #tantheta=y/x# and #r^2=x^2+y^2#.

Hence, #r=4tantheta#

#hArr r^2=16tan^2theta#

#hArrx^2+y^2=16(y^2/x^2)#

or #x^4+x^2y^2-16y^2=0#

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How do you convert #r=4tanθ# into cartesian form?

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