Subtangent ($CE$)

At a point $B$ of a planar curve, let the ordinate through $B$ meet the chosen horizontal coordinate axis at $C$, and let the tangent line at $B$ meet that axis at $E$. The axis segment $CE$ is the subtangent; this construction requires the indicated finite intersection and depends on the chosen axes.

For the standard parabola $y^2=4ax$, $a>0$, take $B=(x_0,y_0)$ with $y_0\ne 0$. The tangent line is $y_{0}y=2a(x+x_0)$, so $E=(-x_0,0)$ and $C=(x_0,0)$. Therefore $CE=2x_0=2CD$, where $D=(0,0)$ is the vertex of a parabola. Here tangent refers to a straight line, rather than the trigonometric tangent function.