I'm stumped by the following question:

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

Method
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See, my train of thought followed as such:

First of all, we see that the two points have the same x value, and thus they probably lie on the circumference of a circle.

$y^{ 2 }+x^{ 4 }=2x^{ 2 }y+1$

$z = { x }^{ 2 }$

$y^{ 2 }-2zy+z^{ 2 }=1$

This simplifies to:
${ (y-z) }^{ 2 }=1$

$y=1+z$

We remember that x = $\sqrt { \pi } $, and since $z={ x }^{ 2 }$, $z=\pi $, y = $1+\pi $. This is where I realized I went wrong somewhere, since |a-b| = 0 at this point. I really have **no idea how to proceed at this point**, as I believed the problem originally required basic algebraic manipulation.