Question

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

Answer 1

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

Answer 2

Can't square both sides?

Answer 3

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

Answer 4

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.

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

\[x ^{2}(x ^{2}+y ^{2})=y ^{2}\] 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.

Answer 11

Find a way to get it?

Answer 12

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

Answer 13

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

Answer 14

Thank you!

Answer 15

mhm :3