AMC 10 2015a Problem 12

Points $( \sqrt{\pi} , a)$ and $( \sqrt{\pi} , b)$ are distinct points on the graph of $y^2 + x^4 = 2x^2 y + 1$. What is $|a-b|$? $\textbf{(A)}\ 1 \textbf{(B)} \ \frac{\pi}{2} \textbf{(C)} \ 2 \textbf{(D)} \ \sqrt{1+\pi} \textbf{(E)} \ 1 + \sqrt{\pi}$