Quick/beginner question on tangent plane. I do know how to do it but...

[eckimz]

I do know how to make tangent plane at a point.

gradient x point x vector = 0
FxPo(X-Xo)+FyPo(Y-Yo)+FzPo(Z-Zo)=0

So the exercise gives us y=x²-z² at P(4,7,3).

My question is, before starting the gradient, do I need to transform y=x²-z² into x²-z²-y=0 to do the partials? Or do I take it as f(y)=x²-z² ???

 

[pka]

I do know how to make tangent plane at a point.

gradient x point x vector = 0
FxPo(X-Xo)+FyPo(Y-Yo)+FzPo(Z-Zo)=0

So the exercise gives us y=x²-z² at P(4,7,3).

My question is, before starting the gradient, do I need to transform y=x²-z² into x²-z²-y=0 to do the partials? Or do I take it as f(y)=x²-z² ???

The form \(\displaystyle x^2-y-z^2=0\) is known as a level curve. You get the gradient from that.
Does that answer your question?

 

[eckimz]

Yes!!

I didn't know if I had to do the partials on y.

Got just the answer on wolframalpha, now I got it how to get there.

I did the partials to fx, fy, applied the point numbers and multiplied by the vector.
gradient(P) x vector = 0
8(x-4)-(y-7)+(-6)(z-3)=0
y= 8x-6z-7.

Thank you again, pka!
(Imma try learn better the html, another time, I know my sheefts are bad haha)