# Polar equation to cartesian equation help

Since this got closed Convert Polar equation to Cartesian coordinates

So I ended up doing some work and I don't know if I'm headed in the right direction, or maybe if I solved it correctly.

problem: $$r\cos(\theta) = 5r^2\sin(2\theta)$$

Steps taken:

\begin{align}x&=10r^2\sin(\theta)\cos(\theta)\\x&=10r\sin(\theta)r\cos(\theta)\\x&=10yx\\y&=1/10\end{align}

Assuming that I'm correct with how to handle converting polar to cartesian, this would be just a horizontal line. I'm confused because I have to give cartesian coordinates, and also describe the curve.

$$x(1-10y)=0$$ describes the curve. So it's two straight lines $$x=0$$ and $$y=\frac{1}{10}$$