Extrema on a curve Find the points on thecurve x 2 +xy+y 2 =1 in the xy-plane th

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Extrema on a curve Find the points on thecurve x2+xy+y2=1 in the xy-plane that arenearest to and farthest from the origin. My work so far: so f(x,y) = x2+y2 and the grad of f is< 2x, 2y > and g(x,y) = x2+xy+y2-1 and the grad ofg is < (2x+y), (x+2y) > Hence < 2x, 2y > = < (2x+y), (x+2y) >because the [grad of f = (grad of g)] I have tried to continue from here, but I just go in circlesand cannot figure out the points nearest and farthest from theorigin. I need help seeing what goes next step by step. Extrema on a curve Find the points on thecurve x2+xy+y2=1 in the xy-plane that arenearest to and farthest from the origin. My work so far: so f(x,y) = x2+y2 and the grad of f is< 2x, 2y > and g(x,y) = x2+xy+y2-1 and the grad ofg is < (2x+y), (x+2y) > Hence < 2x, 2y > = < (2x+y), (x+2y) >because the [grad of f = (grad of g)] I have tried to continue from here, but I just go in circlesand cannot figure out the points nearest and farthest from theorigin. I need help seeing what goes next step by step.

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Thank you for anybody who attempted to solve thisproblem, but I have worked the solution

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