Problem:
Points (π​,a) and (π​,b) are distinct points on the graph of
y2+x4=2x2y+1
What is ∣a−b∣?
Answer Choices:
A. 1
B. 2π​
C. 2
D. 1+π​
E. 1+π​
Solution:
The equation is equivalent to 1=y2−2x2y+x4=(y−x2)2, or y−x2=±1. The graph consists of two parabolas, y=x2+1 and y=x2−1. Thus a and b are π+1 and π−1, and their difference is (C)2​. Indeed, the answer would still be 2 if π​ were replaced by any real number.