directrix's Usage Examples:

14) be two catenaries having the same directrix and intersecting in A and B.

Now let us consider the surfaces of revolution formed by this system of catenaries revolving about the directrix of the two catenaries of equal tension.

x The involute of the catenary is called the tractory, tractrix or antifriction curve; it has a cusp at the vertex of the catenary, and is asymptotic to the directrix.

Hence T, the point of intersection of Pp and Qq, must be the centre of similitude and must be on the common directrix.

The line FL perpendicular to the axis, G D and passing through the focus, is the semilatus rectum, the latus rectum being the focal chord parallel to the directrix.

Then if a pencil be placed along B C so as to keep the string taut, and the limb AB be slid along the directrix, the A pencil will trace out the parabola.

The surface formed by revolving the catenary about its directrix is named the alysseide.

A focus or directrix is equal to two conditions; hence such problems as: given a focus and three points; a focus, two points and one tangent; and a focus, one point and two tangents are soluble (very conveniently by employing the principle of reciprocation).

The line CD passing through the focus and perpendicular to the directrix is the axis or principal diameter, and meets the curve in the vertex G.

"radw b el than"' s o e5 theucr r t ?l t of eg o?pUer, atus 1, ?Any number of points on the parabola are obtained by taking any point E on the directrix, joining EG and EF and drawing FP so that the angles PFE and DFE are equal.

Any number of points on the parabola are obtained by taking any point E on the directrix, joining EG and EF and drawing FP so that the angles PFE and DFE are equal.

Since the tension is measured by the height above the directrix these two catenaries have the same directrix.

Every catenary lying between them has its directrix higher, and every catenary lying beyond them has its directrix lower than that of the two catenaries.