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Question 66

Let $$P(a, b)$$ be a point on the parabola $$y^2 = 8x$$ such that the tangent at $$P$$ passes through the centre of the circle $$x^2 + y^2 - 10x - 14y + 65 = 0$$. Let $$A$$ be the product of all possible values of $$a$$ and $$B$$ be the product of all possible values of $$b$$. Then the value of $$A + B$$ is equal to

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