How do you identify the type of graph generated by the polar equation #r=2asintheta+2acostheta# and what is the equivalent rectangular equation?

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Answer 1 · 2018-01-07T09:31:22

see below

convert to rectangular first

#r^2=x^2+y^2--(1)#

#x=rcostheta--(2)#

#y=rsintheta--(3)#

#r=2asintheta+2acostheta--(4)#

#(4)xxr#

#r^2=2arsintheta+2arcostheta#

using #(1),(2),(3)#

#x^2+y^2=2ay+2ax#

#x^2-2ax+y^2-2ay=0#

complete the square ( the steps are omitted as an exercise for the reader)

#(x-a)^2+(y-a)^2-2a^2=0#

which is a circle centre#" "(a,a)# radius #" "asqrt(2)#