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Finding highest and lowest points on ellipse

Assignment:

The plane, 4*x - 3*y + 8*z = 5, intersects the cone, z^2 = x^2 + y^2, in an ellipse.

Q1. Graph the cone, the plane and the ellipse.

Q2. Using lagrange multipliers find the highest and lowest points on the ellipse.

Please show graphs, equation of the ellipse and all work.

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Mathematics: Finding highest and lowest points on ellipse

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