This problem can be solved using Lagrange multipliers, although my feeling is that your teacher does not want you to solve it this way.  The worksheet that is attached is a modification of the worksheet at this link.  You can use it to get the value of the points, to verify your answer, however to choose to obtain it.  Hint:  You can create a list of x,y pairs for each of your curves(line), and use the square of the sum of squares in a loop to calculate values.  Then look for the minimum.

Download 221_lagrange.mws

Regards,
Georgios Kokovidis
Dräger Medical