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 $theta$ .

How do you convert 2=(2x+3y)^2-x2=(2x+3y)^2-x into polar form?