Finding the distance between a point and a level curve

1. Sep 14, 2009

yeahhyeahyeah

1. The problem statement, all variables and given/known data

Find the point on the curve defined by 5/8 x^2 - 3/4 xy + 5/8 y^2 = 1

That is closest to the point (1,-1)

2. Relevant equations

3. The attempt at a solution

I started by finding the gradient vector. < (5/4x - 3/4 y) , (5/4y - 3/4x) >

I could not figure out if that was even the right direction to go in because I don't know how I'd even find a distance formula

2. Sep 14, 2009

tms

You have one equation with two unknowns, so you need another equation relating those two variables. You do have information to construct another equation: the distance from the curve to the specified point is a minimum. Write down an equation that expresses that condition, and then solve the two equations for the two unknowns.

3. Sep 14, 2009

yeahhyeahyeah

ah nvm i realized its just optimizing a function with another contraining function.. i think... so i could use lagrange multipliers