In practise, it is very difficult to manufacture large parabolic mirrors, which are used in telescopes.

Figure 1: Solar radiotelescope |

It is often necessary to make do with mirrors whose cross section is a portion of a circle approximating the appropriate parabola.

It can be shown that the circle that "best approximates" the parabola near its vertex *V* has its centre *S* located on the axis *o* of parabola twice as far from the vertex *V* as the focus *F* of the parabola and so it has the radius $p=2\left|\overline{VF}\right|=\left|\overline{dF}\right|$ equal to the parabola parameter.

This circle $h=\left(S\mathrm{,}\phantom{\rule{2mm}{2mm}}p\right)$ is called the osculating circle of a parabola in its vertex *V*.

Osculating circle and parabola have common tangent perpendicular to the parabola axis, and the same first curvature in their common point - parabola vertex *V*, see figure.

Figure 2: Parabola with osculating circle |