How do you convert #2=(2x+3y)^2-x# into polar form?

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Answer 1 · 2018-07-13T20:44:21

![ jwilson.coe.uga.edu )

In the diagram above, we can see the relation between the rectangular and polar coordinates of a given point in the plane.

Thus, #2=(2x+3y)^2-x# in polar form is going to be

#2=(2rcostheta+3rsintheta)^2-rcostheta#

Which, after some simplifications, becomes

#2=r^2(4+5sin^2theta+3sin2theta)-rcostheta#

If you want, you can go the extra mile and solve the quadratic equation with undeterminate #r# to write #r# as a function of #theta#.