find the points on the surfaces xy + yz + zx - x- z^2 = 0
where the tangent plane is parallel to the xy-plane?
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
-z0 = (y+x-2z)t
and then ??!!
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 ..