As we tilt the plane off horizontal, the circular cross-section stretches and becomes elliptical.

z^2=x^2+y^2

z=0.5+n*x

vector(x,y,z)=vector(t,plusorminus(sqrt([0.5+n*t]^2-t^2)),0.5+n*t),'radius'=0.05

prime(x)^2+prime(y)^2=[0.5+n*prime(x)]^2

Graph of the formula

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