Can You Solve This?

Question

Here's the equation I need to solve (for $x$)...

$$r\sqrt{x^{2}-r^{2}}+\left(\frac{1}{b}-r^{2}\right)\left(\arccos\left(\frac{r}{x}\right)\right)=\frac{\pi}{2b}$$

is there a solution in terms of the constants $r$ and $b$?

Hmm...

Answer 1

Start by writing $$x=r\sec t$$ This eliminates the square root and the inverse cosine in terms of $\tan t$ and t.