To show that P is the midpoint of AB and CD, we first need to find the coordinates of points A, B, C, and D. The curve is defined by the parametric equations x = ct and y = (c)/(t),

To show that $P$ is the midpoint of $AB$ and $CD$, we first need to find the coordinates of points $A, B, C,$ and $D$. The curve is defined by the parametric equations $x = ct$ and $y = \frac{c}{t}$, where $t>0$ and $c$ is a constant. The point $P$ is given as $\left(cp, \frac{c}{p}\right)$, which means the parameter $t=p$ at point $P$.

1. Find the equation of the tangent at point P.
First, we find the derivatives of $x$ and $y$ with respect to $t$:

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