The plane intersects the paraboloid in an ellipse. Find the points on the ellipse nearest to and farthest from the origin.

So is the goal here to just minimize and then maximize the distance formula with the constraints of and ?

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- Mar 25th 2010, 12:33 PMdavesfaceLagrange Multipliers
The plane intersects the paraboloid in an ellipse. Find the points on the ellipse nearest to and farthest from the origin.

So is the goal here to just minimize and then maximize the distance formula with the constraints of and ? - Mar 25th 2010, 01:11 PMSoroban
Hello, davesface!

Quote:

The plane intersects the paraboloid in an ellipse.

Find the points on the ellipse nearest to and farthest from the origin.

So is the goal to minimize and maximize the distance formula

with the constraints of and ? . . . . Yes!

We have: .

Find the five partial derivatives, equate to zero, and solve the system.

. .

. . . .

I'll wait in the car . . .

. - Mar 25th 2010, 02:16 PMdavesface
I haven't ever seen someone take or (and since those are constants, do those derivatives make sense?). According to my notes, it's set up as , which I think for this problem would be: