Answer
Every tangent plane to the cone passes through the origin $(0,0,0)$.
Work Step by Step
Formula to calculate tangent plane equation for an sphere 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$(x_0,y_0,z_0)$
$(x-x_0)(2x_0)+(y-y_0)(2y_0)-(z-z_0)(2z_0)=0$
This implies,
$xx_0+yy_0-zz_0=x_0^2+y_0^2-z_0^2$
When the tangent plane passes through the origin $(0,0,0)$:
$xx_0+yy_0-zz_0=0$
Thus we have proved that every tangent plane to the cone passes through the origin $(0,0,0)$.