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(C) The equations of the curves are $x^2 + y^2 = 9$ and $y^2 = 8x$.Substituting $y^2 = 8x$ into the circle equation: $x^2 + 8x = 9$.$x^2 + 8x - 9 = 0$

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$L_1 < L_2$

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(C) The equations of the curves are $x^2 + y^2 = 9$ and $y^2 = 8x$.Substituting $y^2 = 8x$ into the circle equation: $x^2 + 8x = 9$.$x^2 + 8x - 9 = 0$.$(x + 9)(x - 1) = 0$.Since $x$ must be non-negative for the parabola $y^2 = 8x$,we have $x = 1$.For $x = 1$,$y^2 = 8(1) = 8$,so $y = \pm 2\sqrt{2}$.The points of intersection are $A(1, 2\sqrt{2})$ and $B(1, -2\sqrt{2})$.The length of the common chord $L_1 = |2\sqrt{2} - (-2\sqrt{2})| = 4\sqrt{2} \approx 5.66$.The parabola $y^2 = 8x$ is of the form $y^2 = 4ax$,where $4a = 8$,so $a = 2$.The length of the latus rectum $L_2 = 4a = 8$.Comparing the values,$4\sqrt{2} < 8$,therefore $L_1 < L_2$.

Let $L_1$ be the length of the common chord of the curves $x^2 + y^2 = 9$ and $y^2 = 8x$,and $L_2$ be the length of the latus rectum of $y^2 = 8x$,then

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