# Can it be shown that gives a conic

Can it be shown that gives a conic section?
${r}^{2}=\frac{1}{1-\epsilon \mathrm{cos}\left(2\theta \right)}$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

PCCNQN4XKhjx
Step 1
Rewrite it as
${r}^{2}\left(1-ϵ\mathrm{cos}\left(2\theta \right)\right)$
$=1⇔{r}^{2}\left(1-ϵ\left({\mathrm{cos}}^{2}\theta -{\mathrm{sin}}^{2}\theta \right)\right)=1$
and then expand. We have

and
${r}^{2}{\mathrm{sin}}^{2}\theta ={y}^{2}$
so we get the traditional equation of an ellipse or a hyperbola.