Question: A tangent line is drawn to the hyperbola xy = c at a point P. (a) Show that the midpoint of the line segment cut

A tangent line is drawn to the hyperbola xy = c at a point P.

(a) Show that the midpoint of the line segment cut from this tangent line by the coordinate axes is P.

(b) Show that the triangle formed by the tangent line and the coordinate axes always has the same area, no matter where P is located on the hyperbola.

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