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(A) The slope $m$ of the line passing through $(ct_1, c/t_1)$ and $(ct_2, c/t_2)$ is given by: $m = \frac{\frac{c}{t_2} - \frac{c}{t_1}}{ct_2 - ct_1}

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$x+t_1 t_2 y=c\left(t_1+t_2\right)$

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(A) The slope $m$ of the line passing through $(ct_1, c/t_1)$ and $(ct_2, c/t_2)$ is given by: $m = \frac{\frac{c}{t_2} - \frac{c}{t_1}}{ct_2 - ct_1} = \frac{c(t_1 - t_2)}{t_1 t_2} \cdot \frac{1}{c(t_2 - t_1)} = -\frac{1}{t_1 t_2}$ Using the point-slope form $(y - y_1) = m(x - x_1)$ with point $(ct_1, c/t_1)$: $y - \frac{c}{t_1} = -\frac{1}{t_1 t_2}(x - ct_1)$ Multiplying both sides by $t_1 t_2$: $t_1 t_2 y - ct_2 = -(x - ct_1)$ $t_1 t_2 y - ct_2 = -x + ct_1$ $x + t_1 t_2 y = c(t_1 + t_2)$

The equation of the line passing through the points $\left(ct_1, \frac{c}{t_1}\right)$ and $\left(ct_2, \frac{c}{t_2}\right)$ is

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