Nice shape

Calculus Level 4

Point A and Point B are \((-1,0)\) and \((1,0)\) respectively. There exists a Point C where \(AC+BC=4\). Given that all of the possible places of Point C forms a shape, and that shape has an area \(A\) that can be expressed as \(b\sqrt { a } \pi \), where \(a\) and \(b\) are co-primes, find the value of \(100(ab)\)

(This is one of my class problems)

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