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

**Answer Choices**

A. 1

B. \dfrac{\pi}{2}

C. 2

D. \sqrt{1+\pi}

E. 1+\sqrt{\pi}

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

**Answer Choices**

A. 1

B. \dfrac{\pi}{2}

C. 2

D. \sqrt{1+\pi}

E. 1+\sqrt{\pi}