R^2 = 8/(2-sin^2 θ) Convert to rectangular form?

[Jurrasic]

Is it right to multiply everything on both sides first, by the (2-sin^2 θ) ? Why would you want to do that? In terms of how it should look, and what variable to solve for, what exactly is the goal here and why?

 

[vela]

Yes, you can do that. When converting to rectangular form, you want to get each sine and cosine multiplied by R because x=R cos θ and y=R sin θ. (I'm assuming you're working with polar coordinates here.) Here you have sin² θ, so you want it multiplied by R², one factor of R for each sine.

 

[eumyang]

In terms of how it should look, and what variable to solve for, what exactly is the goal here and why?

You don't necessarily solve for a variable. The goal is to rewrite the equation so that the variables are x's and y's, not r's and θ's. After multiplying both sides by the denominator, add sin² θ to both sides, and then use the equations that vela gave you. (They are the same one's I mentioned in your previous thread.)