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 $" "asqrt(2)$

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