Question

The plane making intercept 1 at the z-axis and parallel to the xy- plane intersects the cone x^2+y^2=z^2tan^2 ϑ in a circle.
True or false with full explanation

Answer 1

The equation of the circle with center $O(a,b)$ and radius $R$ is $(x-a)^2+(y-b)^2=R^2$. if $z=1$ then the equation of the intersection of the $xy$- plane and the cone $x^2+y^2=z^2tan^2 ϑ$ is $x^2+y^2=\tan^2 ϑ$. So, it is a circle with center $O(0,0,1)$ and radius $R=\tan ϑ$ containing in the plane $z=1$.

Answer: true