A disk of radius 1 is centered at the point $A(0,1,2)$ and is parallel to the plane $xOy$. A source of light is placed at the point $P(0,1,4)$. Characterize analytically the shadow and the disk rushed over the plane $xOy$.
I tried in the next way:
$Oy: x=0,z=0$
$d:y=1,z=4$ to be some generator lines
And then I did the system $y-1-\lambda z=0$ and $z-4-\mu x=0$.
There is also the system for the circle: $x^2+(y-1)^2+(z-2)^2=1$ and $z=2$.
I wrote $x,y,z$ in terms of $\lambda,\mu$ and then replacing again such that: $\lambda=\frac{y-1}{z}$ and $\mu=\frac{z-4}{x}$.
Then, intersecting with $z=0$ I got to $4(y-1)^2=0$, which is a plane. But there should be a disc or an ellipse. Can somebody help me, please?