Call for Co-ordinate?

Calculus Level 5

In the figure, the coordinates of \(A\) are \((0,-7)\) and the co-ordinates of \(B\) are \((-7,0)\). The radius of the circle is \(2\) units. \[\]For points \(P,Q\) on the circle, the maximum value of \(|AP|^2+|PQ|^2+|QB|^2\) is achieved at \[P\left (\dfrac{-a}{b},\dfrac{\sqrt{c}}{b}\right) \text{ and } Q\left (\dfrac{\sqrt{c}}{b},\dfrac{-a}{b} \right )\] Find \(a+b+c\).

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