# 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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