How do you write the equation using rectangular coordinates given #r^2sin2theta=8#?

Question

8631 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-04T09:50:27

#xy=4#

The relation between rectangular Cartesian coordinates #(x,y)# and polar coordinates #(r,theta)# is given by

#x=rcostheta#, #y=rsintheta# and #x^2+y^2=r^2#

Hence #r^2sin2theta=8# can be rewritten as

#r^2xx2sinthetacostheta=8#

or #2xxrsinthetaxxrcostheta=8#

or #2xxyxx x=8#

or #xy=4#