Where should the spotlight be placed ?

A spotlight projects a cone of light of semi-vertical angle $20^{\circ}$ . A Cartesian coordinate system is chosen such that the stage is coincident with the horizontal $xy$ plane. We want the spotlight to generate a light spot on the stage that is an ellipse centered at $(20, 20, 0)$ , has a semi-major axis length of $10$ and a semi-minor axis length of $5$ , such that the major axis makes a counter clockwise angle with the x-axis of $30^{\circ}$ . Where should the spotlight be placed ? If it is to be placed at $P(x, y, z)$ , where $x \gt 20$ , $y \gt 20$ and $z \gt 0$ , and if the splotlight axis direction (towards the stage) in the $xyz$ coordinate frame is along the unit vector $\mathbf{u} = ( u_x , u_y, u_z )$ , then find $x + y + z + 10(u_x + u_y + u_z )$