Prove or disprove: there is at least one straight line normal to the graph of y = cosh x at a point (a, cosh a) and also normal to the graph of y = sinh x at a point (c, sinh c).    

[At a point on a graph, the normal line is the perpendicular
to the tangent at that point. Also, cosh x = (e^x + e¯^x)/2
and sinh x = (e^x - e^-x)/2.]