imc

Note that if the $y$-intercepts have a sum of $0$, the distance from the origin to each of the intercepts must be the same. Call this distance $a$. Since the $\angle PAQ=90^{\circ }$, the length of the median to the midpoint of the hypotenuse is equal to half the length of the hypotenuse. Since the median's length is $\sqrt{6^2+8^2}=10$, this means $a=10$, and the length of the hypotenuse is $2a=20$. Since the $x$-coordinate of $A$ is the same as the altitude to the hypotenuse, $[APQ]=\frac{20\cdot 6}{2}=\boxed{60}$.