AMC 12B 2005 Problem 8

Past Contests AMC 12 AMC 12B - 2005
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1

For how many values of a is it true that the line y=x+a passes through the vertex of the parabola y=x^{2}+a^{2} ?

Answer Choices
A. 0
B. 1
C. 2
D. 10
E. infinitely many