tangent plane: got lost on the math

[eckimz]

find the tangent plane to the surfices at the point
z= √4-x²-2y² at (x,y,z)=(1, -1, 1)

gradient(P) x vector = 0

vector = <x-1, y+1, z-1>
partials to x
Fx= - x√4-x²-2y²/4-x²-2y²
Fy= -2y√4-x²-2y²/4-x²-2y²

Applied x=1 and y=-1

Got,

√-2y²+3/-2y²+3 : for X

2√2-x²/2-x² : for Y

Ok, now I started crying on my math.

(√-2y²+3/-2y²+3) * (x-1) + (2√2-x²/2-x²) * (y+1) - (z-1)= 0

Is this right?! Ive done the math for it on symbolab, gets pretty ugly and on walfram says

is the answer.
Can the above equation turn into

?

(Ive checked the partials, its good)

Any thoughts?

 

[pka]

find the tangent plane to the surfices at the point
z= √4-x²-2y² at (x,y,z)=(1, -1, 1)

Have you posted the problem correctly? The point \(\displaystyle (1,-1,1)\) is not on the surface \(\displaystyle z=\sqrt4-x^2-2y^2\)

 

[LCKurtz]

find the tangent plane to the surfices at the point
z= √4-x²-2y² at (x,y,z)=(1, -1, 1)

I suppose you mean [MATH]z = \sqrt{4 - x^2 -2y^2}[/MATH]. If you aren't going to use TeX you must learn to use parentheses properly.

The rest of your post below is a jumbled mess of nonsense. Square your equation to get rid of the square root and get the equation in the form [MATH]f(x,y,z) = C[/MATH]. Then calculate the normal vector [MATH]\vec N = \nabla f(P)[/MATH] for your point. Come back when you have done that.

gradient(P) x vector = 0

vector = <x-1, y+1, z-1>
partials to x
Fx= - x√4-x²-2y²/4-x²-2y²
Fy= -2y√4-x²-2y²/4-x²-2y²

Applied x=1 and y=-1

Got,

√-2y²+3/-2y²+3 : for X

2√2-x²/2-x² : for Y

Ok, now I started crying on my math.

(√-2y²+3/-2y²+3) * (x-1) + (2√2-x²/2-x²) * (y+1) - (z-1)= 0

Is this right?! Ive done the math for it on symbolab, gets pretty ugly and on walfram says

is the answer.
Can the above equation turn into

?

(Ive checked the partials, its good)

Any thoughts?

 

[eckimz]

Thanks, got the results!

 

[LCKurtz]

This thread is exhibit A on how not to behave when asking for help in a thread.
1. Create an indecipherable post.
2. When pointed out that a given point is not on the surface (a hint that his equations need rewriting), ignore it.
3. When given a more direct observation about the need to use parentheses, ignore it.
4. When given a suggestion on a better approach to the problem, ignore it.
5. When finally returning to the thread, just say you have solved it, with no explanation or acknowledgement that you have understood anything posted by the helpers. Mark it as solved and disappear.

 

[eckimz]

This thread is exhibit A on how not to behave when asking for help in a thread.
1. Create an indecipherable post.
2. When pointed out that a given point is not on the surface (a hint that his equations need rewriting), ignore it.
3. When given a more direct observation about the need to use parentheses, ignore it.
4. When given a suggestion on a better approach to the problem, ignore it.
5. When finally returning to the thread, just say you have solved it, with no explanation or acknowledgement that you have understood anything posted by the helpers. Mark it as solved and disappear.

1. This is one of my first thread on the forum, it was approved by someone. I'm learning to use TeX, you don't need to be rude about it. You could just see how many messages I had... I'm on exams week and I'm constantly doing loads of homework. I'm really trying to get better here, but seems there is no place for mistakes around.

2. I didn't ignored you or PKA, you assumed it right and I gave it a like, so you can pressume I saw it.
It was badly writting due my almost zero knowledge on how to write squares, fractions in TeX. And your hint was also right, with that said you solved my doubt and I thank you, cause you SOLVED my doubt. I was doing it wrong due the square.

3. My text might not be good, but it shows I do know the process to do tangent plane and with that said adding your comment on the square, it shows I was clearly doing it wrong on basic math. When you pointed out the square, I instantly fixed and I did not think for a second that should be explained. At this point, I apologize, I should've said: "Hey, thanks, you were right, I solved".

4. I did not ignored, I apologize again for doing a dynamic quick reply. (exams week).

5. So, finally, I marked as solved, cause it was solved and didn't feel right to leave it unsolved, I did not want helpers to come look this, when I had it solved. I just thought you'd pressume that your hint was right, otherwise I'd say something else instead of thanks.

And I didn't disappear, I moved to another problems and if you surf though calculus forum, I did MANY posts with doubts and I did write it better on TeX (and lately someone told me I can learn tex codes by clicking on reply), I did put my work step by step.

This kind comment, just make me not want to post or ask for help. I'm new here and I will learn it how to ask and help (if I can) better eventually, otherwise, how could helpers help out?!

I understand that forum has standards and I really tried to keep it and I think I already got the way of it, but come on, one more time, this was my THIRD THREAD.