Question 108
a) Find all real numbers $a$ such that the parabola $y = x^2 - a$ and the hyperbola $y = 1/x$ intersect each other in three different points.
b) Find the locus of the centers of circumcircles of such triples of intersection points when $a$ takes all possible values.
b) Find the locus of the centers of circumcircles of such triples of intersection points when $a$ takes all possible values.