Question

How would you find the following. A step by step process would greatly be appreciated.

1) Convert the polar equation to a rectangular equation.

r^2 = 8sin2θ

Answer 1

hints:
use the relations:
x=rsinθ
y=rcosθ
which means the left-hand side
=x²+y²=r²

Also
8sin2θ = 16 sinθcosθ
=16(y/r)(x/r)
=16xy/r²

Equating both sides,
x²+y² = 16xy/r²
or
(x²+y²)² = 16xy
=2xy/(x²+y²)

Answer 2

Thank you so much. I was stuck on the right hand side with the 8sin2θ. Not sure what to do with the 8 and 2.

This has cleared it up very well.