hi

Question:

find the points on the surfaces xy + yz + zx - x- z^2 = 0

where the tangent plane is parallel to the xy-plane?

my solution:

tangent line is parallel to xy-plane = normal line to surface orthognal to xy-plane

since normal line is orthognal to xy-plane that mean its intersect xy-plane

and the normal is gradient f

all what i will do is finding the parametric equation of the normal line and putting z=0

equation of normal line:

x = x0 + (y+z-1) t

y = y0 + (x+z) t

z = z0 + (y+x-2z) t

putting z=0

-z0 = (y+x-2z)t

and then ??!!

Edit:

i saw question like this .. but it was given a point at which the normal line starts from

i.e. x0,y0 and z0 are known ..