The square distance from some point ab to some other point x

The square distance from some point (a,b) to some other point (x,y) is (x-a)^2+(y-b)^2.

a) Use Lagrange multipliers that minimizes the distance if the point (x,y) is on the line y-x=0

b) Use Lagrange multipliers that minimizes the distance if the point (x,y) is on x^2-y^2=0

c) compare Lagrange multipliers in parts a) and b). Why are they different?

6. The square distance from some point (a.b) to some other point (x,y) is (x-a)+(y-b). a) Use Lagrange multipliers that minimizes the distance if the point (x,y) is on the line y-x-0 b) repeat part a) with constrain x2-y2-0 c) compare Lagrange multipliers in parts a) and b). Why are they different?

Solution