Problem:
Points (Οβ,a) and (Οβ,b) are distinct points on the graph of
y2+x4=2x2y+1
What is β£aβbβ£?
Answer Choices:
A. 1
B. 2Οβ
C. 2
D. 1+Οβ
E. 1+Οβ
Solution:
The equation is equivalent to 1=y2β2x2y+x4=(yβx2)2, or yβx2=Β±1. The graph consists of two parabolas, y=x2+1 and y=x2β1. Thus a and b are Ο+1 and Οβ1, and their difference is (C)2β. Indeed, the answer would still be 2 if Οβ were replaced by any real number.