Find an equation in x and y that has the same graph as the polar equation:
r = tan theta

Question

Find an equation in x and y that has the same graph as the polar equation:
r = tan theta

anonymous · Answer

$$r = \tan \theta$$$$r = \frac{ r \sin \theta }{ r \cos \theta }$$$$r =\frac{ y }{ x }$$But what next?

psymon · Answer

Can't square both sides?

anonymous · Answer

$$x^2 + y^2 = \frac{ y^2 }{ x^2 }$$ how could you simplify that?

psymon · Answer

You don't. I'm not going to say I'm certain that's correct, but when you get things like x^2 + y^2 = x, you just leave it, lol.

anonymous · Answer

Is there a way to put it in terms of y?

psymon · Answer

Does your question explicitly require it? An answer like that I'd probably just leave as is. I'll be corrected if I'm wrong, but if we have that there is no real simplifying it.

anonymous · Answer

Well, is$$x^2 + y^2 = \frac{ y^2 }{ x^2 }$$a different way of saying$$y^2 = \frac{ x^4 }{1-x^2 }$$because thats the answer in the back of the book

psymon · Answer

Ah. Gotcha. Yes, it can be written in that way :3

anonymous · Answer

Can you help me get it to that point? Please?

psymon · Answer

$$x ^{2}(x ^{2}+y ^{2})=y ^{2}$$ I multiplied x^2 out of the denominator. Now you need to distribute the x^2 and collect all the y terms on one side of the equation.

psymon · Answer

Find a way to get it?

anonymous · Answer

Yeah, so $$x^4 + y^2x^2 = y^2$$$$x^4=y^2-y^2x^2$$$$x^4=(1-x^2)y^2$$$$y^2=\frac{ x^4 }{ 1-x^2 }$$

psymon · Answer

Right ^_^ Just was making sure. Good job.

anonymous · Answer

Thank you!

psymon · Answer

mhm :3