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## lagrange multipliers

Find the shortest and longest distance from the origin to the curve
$$x^2 + xy + y^2=16$$ and give a geometric interpretation...the hint given is to find the maximum of $$x^2+y^2$$

i am not sure what to do for this problem

thanks

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Quote by thenewbosco 					 				 				Find the shortest and longest distance from the origin to the curve  $$x^2 + xy + y^2=16$$ and give a geometric interpretation...the hint given is to find the maximum of $$x^2+y^2$$  i am not sure what to do for this problem  thanks
Are you sure you need Lagrange Multipliers for this?

it says for the hint to use the method of lagrange multipliers to find the maximum of $$x^2 + y^2$$ but i am not sure how to do it using any method, so any help is appreciated.

## lagrange multipliers

Quote by thenewbosco 					 				 				it says for the hint to use the method of lagrange multipliers to find the maximum of $$x^2 + y^2$$ but i am not sure how to do it using any method, so any help is appreciated.
Solve for y. use rate of change respect to the distance.
that is the "cal 1 method"

the path equation is constraint i think. apply Lagrange Multipliers on the distance formula

solve for y in what though. in the question it says $$x^2+y^2$$ this isnt even an equation though.  im sorry i still dont get it

Quote by thenewbosco 					 				 				solve for y in what though. in the question it says $$x^2+y^2$$ this isnt even an equation though.  im sorry i still dont get it
you can solve for y in tern of x
and then using the distance formula D = (y^2+x^2)^0.5
sub the y equation into the distance formula
take the first derivative
fine 0s
test it
done

that is cal 1 method, it requires a lot of work

$$x^2+y^2$$ looks really similar to the distance formula
$$D^2 = x^2 + y^2$$

you can set $$D = f(x)$$ or $$D^2 = f(x)$$ and find the del of it, since the square doesnt where the extreme occurs, therefore the text tells you to fine the max of $$x^2+y^2$$

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