PUTNAM EXAM CHALLENGE
From the vertex (0, c) of the catenary cosh(x/c) a line L is drawn perpendicular to the tangent to the catenary at point P. Prove that the length of L intercepted by the axes is equal to the ordinate y of the point P.
To prove: The length of L intercepted by the axis is equal to the ordinate of the point P.
A line L drawn perpendicular to the tangent to the catenary at a point P from the vertex of the catenary.
The Pythagoras theorem for triangle and formula for equation of line when a point and slope is provided, i.e. where is the provided point and m is the slope if the line.
As provided, the catenary . Consider, be a point on the catenary.
is the slope of the line at the
Therefore, the equation of the line L;
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