1. The problem statement, all variables and given/known data Using the method of lagrange multipliers, find the points on the curve 3x² - 4xy + 6y² = 140 which are closest and furthermost from the ORIGIN and the corresponding distances between them 3. The attempt at a solution I have done roughly half the question but appear to be stuck! Firstly I find distance from a point (x,y) to the (0,0) using distance equation. This yields: d² = x² + y² = f(x,y) My constraint equation is given by the equation of the curve given, i.e. g(x,y) = 3x² - 4xy + 6y² = 140 Now I want to use grad(f) = λgrad(g) Therefore; 2xi + 2yj = λ[(6x-4y)i + (-4x+12y)j] And by equating coefficients, 2x = λ(6x-4y) (1) 2y = λ(-4x+12y) (2) This is where I get stuck, I have never encountered a problem like this whereby one of the variables depends on itself. What is the best way to tackle this? Should I sub (1) into (2)?