Finding the distance between a point and a level curve

[yeahhyeahyeah]

Homework Statement

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)

Homework Equations

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

 

[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.

 

[yeahhyeahyeah]

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

thanks for your help