An Elementary Treatise on the Geometry of ConicsMacmillan & Company, 1893 - 184 páginas |
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An Elementary Treatise on the Geometry of Conics Sir Asutosh Mookerjee No hay ninguna vista previa disponible - 2015 |
Términos y frases comunes
angle Q'Sq Apply Ex Apply Prop auxiliary circle axes axis in G bisects the angle CA² CB² centre Chap chord QQ circle described coincide conic conjugate axis conjugate diameters conjugate hyperbola conjugate semi-diameters describe a circle diameter bisecting draw PM drawn parallel ellipse equally inclined exterior angle external point Find the locus fixed point fixed straight line focal chord focal distances focal perpendiculars foci Given a focus given point latus rectum Let the tangent line drawn line joining major axis meet the curve meet the directrix meet the major meeting the asymptotes middle point minor axis normal parabola parallel chords parallel to QQ PN² point of intersection points of contact produced meet PROPOSITION Prove rectangle rectangular hyperbola respectively right angles segments similar triangles subtends a right tangent at Q transverse axis vertex XXIII
Pasajes populares
Página 12 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Página 10 - Find the locus of the middle points of any system of parallel chords in a circle.
Página 75 - ... either end of a diameter is parallel to the system of chords bisected by the diameter. The portion of the tangent at any point intercepted between that point and the directrix subtends a right angle at the focus and conversely. The tangents at the ends of a focal chord intersect on the directrix. The tangent at any point of an ellipse makes equal angles with the focal distances of the point. (c) Solid Geometry. One and only one plane may be made to pass through any two intersecting straight lines....
Página 6 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.
Página 143 - An ellipse and a hyperbola are described so that the foci of each are at the extremities of the transverse axis of the other; prove that the tangents at their points of intersection meet the conjugate axis in points equidistant from the centre.
Página 86 - P, they enclose a part of one of the focal distances of that point equal to the other. 26. If P be a fixed point on .an ellipse, and QQ' an ordinate to CP, the circle QPQ' will meet the ellipse in a fixed point.
Página 174 - Given the base of a triangle and the difference of the angles at the base, to determine the locus of the vertex. Taking the same axes as before, and putting a, a', for the tangents of the angles at the base, and t for the tangent of their difference, we a _ a...
Página 55 - That is : the sum of the focal distances of any point on an ellipse is constant and equal to the major axis.
Página 161 - P in an hyperbola draw a straight line, such that the segment intercepted between the other intersection with the hyperbola and a given asymptote shall be equal to a given line.
Página 67 - Through a fixed point 0 any straight line is drawn meeting two given parallel straight lines in P and Q ; through P and Q straight lines are drawn infixed directions, meeting in E: prove that the locus ofR is a straight line.