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2015 AMC 10A Question 12

AMC10 · 2015 AMC 10A

Question 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 $|a-b|?$
  1. $1$
  2. $\dfrac{\pi}{2}$
  3. $2$
  4. $\sqrt{1+\pi}$
  5. $1 + \sqrt{\pi}$