You have to minimize the function with the constraight ... a classical problem involving Lagrange's multipliers...
Kind regards
Hello, I am trying to find the closest point on the circle x^2+y^2=1 to (1,2) using calculus, not geometry. However, when I try, I get:
x^2+y^2=1
y=sqrt(1-x^2)
trying to find the distance between (x,sqrt(1-x^2)) and (1,2) = (1-x, 2-sqrt(1-x^2))
d=sqrt((1-x)^2+(2-sqrt(1-x^2))^2)
d=sqrt(1-x^2+4-1+x^2)
d=sqrt(5)
Simple geometry tells me this is the distance between the two points, so how do I solve for x and y from here?