Polar equation to rectangular equation, help please?

r=2asin(theta)+2acos(theta)

I know that r=sqrt(x^2+y^2), but I can't figure out what to do after that point.

Question

Polar equation to rectangular equation, help please?

r=2asin(theta)+2acos(theta)

I know that r=sqrt(x^2+y^2), but I can't figure out what to do after that point.

anonymous · Answer

$$x=r \cos \theta,\cos \theta=\frac{ x }{ r },y=r \sin \theta,\sin \theta=\frac{ y }{ r}$$
substitute and solve.

anonymous · Answer

you followed

anonymous · Answer

Not really... I did this:

sqrt(x^2+y^2)=2asin(theta)+2acos(theta)
x^2+y^2=2a^2sin(theta)+2a^2cos(theta)
x^2+y^2=2a^2(y/r)+2a^2(x/r)

But that seems wrong and I don't know what to do after that?

anonymous · Answer

$$r=\frac{ 2ay }{ r }+\frac{ 2ax }{r },r^2=2a \left( y+x \right)$$

anonymous · Answer

you got it.

anonymous · Answer

My answer key says it should be (x-a)^2+(y-a)^2=2a^2 ?

anonymous · Answer

x^2+y^2-2ax-2ay=0
complete the squares.

anonymous · Answer

Ohh okay! Thank you so much for your help! :)

anonymous · Answer

yw