Question

Convert the polar equation r 2 = 2tan θ to a Cartesian equation.

Answer 1

Is that
\[r^2=2\tan(\theta)\]

Answer 2

yes

Answer 3

okay the answer I have is x^2+y^2=2y

Answer 4

that should be right

Answer 5

Thats what I thought but the thing says its wrong.

Answer 6

rightly so.
It doesn't get any better than when your polar equation is expressed only in terms of
\(r^2\) and \(\tan \theta\)
Because they're readily replaceable

Answer 7

r^2 = x^2+y^2
and tan theta = y/x
so, shouldn't it be
x^2+y^2 = 2y/x ?

Answer 8

No My school program says its x^3+xy^2=2y, but that makes no sense at all.

Answer 9

x= r cos A
y= r sin A

\[ \tan A= \frac{\sin A}{\cos A}= \frac{r \sin A}{r \cos A}= \frac{y}{x} \]
\[ r^2 = x^2 + y^2 \]
so you have
\[ r^2 = 2 \tan A \\ x^2+y^2 = \frac{2y}{x} \\ x^3 + xy^2 = 2y \]

Answer 10

x^2+y^2 = 2y/x
got this ?
then just multiply x on both sides

Answer 11

okay that makes sense

Answer 12

Thanks All!