# Directrix Sentence Examples

- Focus by two tangents drawn from a point), and (having given the focus and a double ordinate) he uses the focus and
**directrix**to obtain any number of points on a parabola - the first instance on record of the practical use of the**directrix**. - The surface formed by revolving the catenary about its
**directrix**is named the alysseide. - 1, where P is a point on the curve equidistant from the fixed line AB, known as the
**directrix**, and the fixed point F known as the focus. - 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. - 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. - 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. - Again, if a chain pass over a perfectly smooth peg, the catenaries in which it hangs on the two sides, though usually of different parameters, wifi have the same
**directrix**, since by (10) y is the same for both at the peg. - The tangents at the ends meet on the
**directrix**, and their inclination to the horizontal is 56 30. - 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. - 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. - Hence a catenoid whose
**directrix**coincides with the axis of revolution has at every point its principal radii of curvature equal and opposite, so that the mean curvature of the surface is zero. - 14) be two catenaries having the same
**directrix**and intersecting in A and B. - Draw Pp and Qq touching both catenaries, Pp and Qq will intersect at T, a point in the
**directrix**; for since any catenary with its**directrix**is a similar figure to any other catenary with its**directrix**, if the**directrix**of the one coincides with that of the other the centre of similitude must lie on the common**directrix**. - Also, since the curves at P and p are equally inclined to the
**directrix**, P and p are corresponding, points and the line P p must pass through the centre of similitude. - Hence the tangents at A and B to the upper catenary must intersect above the
**directrix**, and the tangents at A and B to the lower catenary must intersect below the**directrix**. - A conic section (or as we now say a " conic ") is the locus of a point such that its distance from a given point, the focus, is in a given ratio to its (perpendicular) distance from a given line, the
**directrix**; or it is the locus of a point which moves so as always to satisfy the foregoing condition. - Eccentricity less than unity: this involves the notion of one
**directrix**and one focus; (2) the ellipse is the locus of a point the sum of whose distances from two fixed points is constant: this involves the notion of two foci. - To investigate the form of the curve use may be made of the definition: the ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point (the focus) to its distance from a straight line (the
**directrix**) is constant and is less than unity. - I) be the
**directrix**, S the focus, and X the foot of the perpendicular from S to KX. - Line K'X' parallel to KX such that AX = A'X', then the same curve will be described if we regard K'X' and S' as the given
**directrix**and focus, the eccentricity remaining the same. - The square on the semi-major axis equals the rectangle contained by the distances of the focus and
**directrix**from the centre; and 2a = SP+S'P, where P is any point on the curve, i.e. - 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). - Of practical importance are the following constructions: - (I) Given the axes; (2) given the major axis and the foci; (3) given the focus, eccentricity and
**directrix**; (4) to construct an ellipse (approximately) by means of circular arcs. - 2) be the focus, KX the
**directrix**, X being the foot of the perpendicular from S to the**directrix**. - Take any point R on the
**directrix**, and draw the lines RAM, RSN; draw SL so that the angle LSN =angle NSA'. - For, draw through P a line parallel to AA', intersecting the
**directrix**in Q and the line RSN in T. - One definition, which is of especial value in the geometrical treatment of the conic sections (ellipse, parabola and hyperbola) in piano, is that a conic is the locus of a point whose distances from a fixed point (termed the focus) and a fixed line (the
**directrix**) are in constant ratio. - In the case of the circle, the centre is the focus, and the line at infinity the
**directrix**; we therefore see that a circle is a conic of zero eccentricity. - His proofs are generally long and clumsy; this is accounted for in some measure by the absence of symbols and technical terms. Apollonius was ignorant of the
**directrix**of a conic, and although he incidentally discovered the focus of an ellipse and hyperbola, he does not mention the focus of a parabola.