How do you convert #y=4x-7# into polar form?

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Answer 1 · 2016-06-27T02:38:27

#y=4x-7# is equivalent to #color(red)(r=7/(4*cos theta-sin theta))#

We start with the given equation #y=4x-7#

We should know that equivalent of #x#

#x=r cos theta#

We should also know that equivalent of #y#

#y=r sin theta#

#y=4x-7#

#r sin theta=4(r cos theta)-7#

#r sin theta-4*r cos theta=-7#

#r(sin theta-4*cos theta)=-7#

#r=(-7)/(sin theta-4*cos theta)#

#r=7/(4*cos theta-sin theta)#

Kindly see the graph of #r=7/(4*cos theta-sin theta)#

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God bless....I hope the explanation is useful.