View source for Curve of pursuit

A curve representing a solution of the  "pursuit"  problem, which is posed as follows: Let a point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027400/c0274001.png" /> be moved uniformly along a given curve. The trajectory has to be found of the uniform movement of a point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027400/c0274002.png" />, such that the tangent drawn towards the trajectory at any moment of the movement would pass through the position of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027400/c0274003.png" /> corresponding to that moment in time.

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/c027400a.gif" />

Figure: c027400a

In a plane, the system of equations which the curve of pursuit must satisfy takes the form

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027400/c0274004.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027400/c0274005.png" /> is the slope of the curve of pursuit, and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027400/c0274006.png" /> is the equation of the given curve.

The  "pursuit"  problem was posed by Leonardo da Vinci and solved by P. Bouguer (1732). For a generalization of it see the last Chapter of [[#References|[2]]].

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,   "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  J.E. Littlewood,   "A mathematician's miscellany" , Methuen  (1953)</TD></TR></table>