# Lagrange Multipliers

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

1. Graph the cone, the plane and the ellipse

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

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

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The Cone-Plane system looks like:

And the ellipse is clearly visible from a top view:

We are interested at the points on the ellipse that have the minimal and maximal ...

#### Solution Summary

The highest and lowest points of an ellipse that results from intersection of a plane with a cone are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.