# Thread: Find the equation of the level surface through (-1,2-1)

1. ## Find the equation of the level surface through (-1,2-1)

Hi,

The question is: Find the eq. of the level surface through point p= (1,2,-1) and find the eq of the straight line in R3 which is normal to this surface at p

Is finding the equation of the level surface to f(x,y,z) = x^2 - y^2 + z^2 at point (-1,2,-1) the same as finding the equation of the tangent plane to the surface at that point?

Thanks for any help!

2. Originally Posted by Ant
The question is: Find the eq. of the level surface through point p= (1,2,-1) and find the eq of the straight line in R3 which is normal to this surface at p

Is finding the equation of the level surface to f(x,y,z) = x^2 - y^2 + z^2 at point (-1,2,-1) the same as finding the equation of the tangent plane to the surface at that point?
No it is not. It simply means writing the equation $f(x,y,z)=K$ where $K$ is a constant.

So in this case we have $f(x,y,z)=f(-1,2,-1)$.

3. So here we have $K = -2$ ?

4. I also have that the equation to of the straight line normal to this surface at p is:

$t (2i -4j -2k)$ where t is a scalar variable.

Can anyone say if i'm on the right track here? Thanks

5. Originally Posted by Ant
I also have that the equation to of the straight line normal to this surface at p is:

$t (2i -4j -2k)$ where t is a scalar variable.

Can anyone say if i'm on the right track here? Thanks
You forgot the point: $<-1,2,-1>+t <-2i -4j -2k>$

6. Of course! Thanks again