I 'd like to see the steps it takes to solve each of these problems. Thanks!

Polar to Rectangular:

1.) r^{2}= sin2θ

2.) r = 2secθ ( i got x=2, not sure if it's right)

3.) r = 6/(2cosθ - 3sinθ)

Rectangular to Polar:

1.) 2xy=1

2.) y^{2}- 8y - 16 = 0

3.) x^{2}+ y^{2 }- 2ay = 0

4.) x^{2}= y^{3}( my final answer is r= cot^{2}θcscθ )