+130558 Have a look at this graph, Melody.
https://www.desmos.com/calculator/blatwtgdae
I have graphed the tangent line to the curve at (1/√2, 3/2) and a line perpendicular to this one that goes through the same point. And the perpendicular line also goes through (0,2). And the shortest distance between a line and a point is a perpendicular line to the given line passing through that point....
{The same argument can be made for the other point (-1/√2, 3/2)...}
