# Lagrange multipliers

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

amcavoy
thenewbosco said:
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?

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.

leon1127
thenewbosco said:
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

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thenewbosco
solve for y in what though. in the question it says $$x^2+y^2$$ this isn't even an equation though.
I am sorry i still don't get it

leon1127
thenewbosco said:
solve for y in what though. in the question it says $$x^2+y^2$$ this isn't even an equation though.
I am sorry i still don't 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 doesn't where the extreme occurs, therefore the text tells you to fine the max of $$x^2+y^2$$

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