#### Answer

Every tangent plane to the cone passes through the origin $(0,0,0)$.

#### Work Step by Step

Our aim is to determine the tangent plane equation for an ellipsoid.
The general form is: $(x_2-x_1)f_x(x_1,y_1,z_1)+(y_2-y_1)f_y(x_1,y_1,z_1)+(z_2-z_1)f_x(x_1,y_1,z_1)=0$ ...(1)
From the given data, we have $f(x,y,z)=(x_0,y_0,z_0)$
Equation (1), becomes:
Thus,
$(x-x_0)(2x_0)+(y-y_0)(2y_0)-(z-z_0)(2z_0)=0$
After simplifications, we get $xx_0+yy_0-zz_0=x_0^2+y_0^2-z_0^2$
Tangent plane is passing through the origin $(0,0,0)$, therefore
$xx_0+yy_0-zz_0=0$
It is proved that every tangent plane to the cone passes through the origin $(0,0,0)$.