Answer
No
Work Step by Step
Formula to calculate tangent plane equation is:
$(x_2-x_1)f_x(x_1,y_1,z_1)+(y_2-y_1)f_y(x_1,y_1,z_1)+(z_2-z_1)f_x(x_1,y_1,z_1)=0$
At point$(1,1,-1)$
$(x-x_0)(2x)+(y-y_0)(-2y)+(z-z_0)(-2z)=0$
There must exist a constant number $p$ when the planes are parallel.
Thus,
$(\dfrac{p}{2})^2-(-\dfrac{p}{2})^2-(-\dfrac{p}{2})^2=-\dfrac{p^2}{4}$
which has no solution.
Hence,
There are no points on the hyperboloid.
