Please help me with this problem, as soon as possible.
Find the point on the curve x^2/4 + y^2 = 1 which is as close as possible to the line y = 5 -x.
The hint on the problem says one way of minimize the distance between 2 curves is to pick generic points on both curves and the minimize the (square of ) the distant between 2 points.
I can't think of anything at all except the fact that the shortest distance between 2 curves are always along the line that is normal to both of them.
I have no idea where to start. Someone, Please, help me with this. Thank you!