Question

Please help me solve the following problem. Let z=3x^2-y^2. Find all points at which the magnitude of the gradient of z equals 6.

Answer 1

\[z=3x^2-y^2\]

Answer 2

Let's take its gradient :D

Answer 3

<6x,-2y>

Answer 4

oh... okay, great :D

Answer 5

I suppose you also worked out its magnitude? :)

Answer 6

yea...
do i find x and y in the following equation?
\[x^2+\frac{ y^2 }{ 9 }=1\]

Answer 7

OH, I see, were you TRYING to find specific values for x and y? :)

Answer 8

i looked in the back of the book and the answer is an equation so i guess I'm not supposed to find exact values

Answer 9

No, in fact, I think this is enough, just add a little description :)
From your vast precalculus experience, I hope you know that this equation represents an ellipse :D

Answer 10

The answer in the back of the book is :
\[9x^2+y^2=9\]

So my answer is essentially the same

Answer 11

yes i know it is an ellipse

Answer 12

Well then, that was it :)

Answer 13

thanks

Answer 14

So a complete answer would be:
The points at which the magnitude of the gradient of z equals 6 are contained on the ellipse given by the equation....(my original equation)

Answer 15

Yes. (It IS an ellipse, right? Suddenly I'm not so sure of myself D: )

^_^

Answer 16

ya